MM255 Ch12

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Get Out of Debt Diet

12-1 Installment Loans and Closed-End Credit

1. Find the amount financed, the installment price, and the finance charge of an installment loan.

2. Find the installment payment of an installment loan. 3. Find the estimated annual percentage rate (APR) using a table.

12-2 Paying a Loan Before It Is Due: The Rule of 78

1. Find the interest refund using the rule of 78.

12-3 Open-End Credit

1. Find the finance charge and new balance using the average daily balance method.

2. Find the finance charge and new balance using the unpaid or previous month’s balance.

Having trouble paying your bills? Constantly making mini- mum payments each month? Don’t know how much you owe? Worried about getting a bad credit report? According to Index- CreditCards.com, the average U.S. household has credit card debt of over $7,300, with interest rates ranging from the mid- dle to high teens. Credit card companies have made running up that balance deceptively easy.

However, there are a number of steps you can take to pay off the debt and get back on track. Of course, this will require you to adjust your spending habits and become more careful about your spending.

1. Determine what you owe. Make a list of all the debts you have including the name of the creditor, your total balance, your minimum monthly payment, and your interest rate. This will help you determine in which order you should pay down your debts.

2. Pay it down. Work overtime or take on a second job and devote that income to paying down debt. Cash in CDs, pay down home equity loans, and pay down loans against retire- ment. Have a garage sale. Do whatever you can to earn extra money and devote that money to paying down your debt.

3. Reduce expenses. Eliminate any unnecessary expenses such as eating out and expensive entertainment. Clip coupons, shop at sales, and avoid impulse purchases. Brown bag it at work and be creative about gifts. Above all, stop using credit cards. Just giving up that expensive cup of coffee each morning can save you more than $750 dollars a year.

4. Record your spending. This is actually your key to getting out of debt. You’re in debt because you spent money you didn’t have. Avoiding more debt starts with knowing what you are spending your money on. Each day for at least one month, write down every amount you spend, no matter how small. Reviewing how you spend your money allows you to set priorities.

5. Make a budget based on your spending record. Write down the amount you spent in each category of spending last month as you budget for spending for the next month. Categorize your monthly expenses into logical groups such as necessities (food, rent, medicine, pet food, and so on), should have (things you need but not immediately, such as new workout gear), and like to have (things you don’t need but enjoy (magazines, cable television). One expense should be paying off your debt. Did you know that making a minimum payment of $26 on a single credit card with a $1,000 balance and 19% interest will take more than five years to pay off?

6. Pay cash. This results in a significant savings in terms of what you purchase and not having to pay interest on those purchases. When you don’t have the cash, you don’t buy.

7. Resolve to spend less than you make. Realize once and for all that if you can’t pay for it today then you can’t afford it.

Managing your credit and knowing exactly how much you are paying for using credit are important concepts that you will learn in this chapter.

Two corresponding Business Math Case Videos for this chapter, Which Credit Card Deal is Best? and Should I Buy or Lease a Car? can be found online at www.pearsonhighered.com\cleaves.

LEARNING OUTCOMES

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Many individuals and businesses make purchases for which they do not pay the full amount at the time of purchase. These purchases are paid for by paying a portion of the amount owed in regular payments until the loan is completely paid. This type of loan or credit is often referred to as consumer credit.

In the preceding chapters we discussed the interest to be paid on loans that are paid in full on the date of maturity of the loan. Many times, loans are made so that the maker (the borrower) pays a given amount in regular payments. Loans with regular payments are called installment loans.

There are two kinds of installment loans. Closed-end credit is a type of loan in which the amount borrowed plus interest is repaid in a specified number of equal payments. Examples in- clude bank loans and loans for large purchases such as cars and appliances. Open-end credit is a type of loan in which there is no fixed number of payments—the person keeps making pay- ments until the amount is paid off, and the interest is computed on the unpaid balance at the end of each payment period. Credit card accounts, retail store accounts, and line-of-credit accounts are types of open-end credit.

Consumer credit: a type of credit or loan that is available to individuals or businesses. The loan is repaid in regular payments.

Installment loan: a loan that is repaid in regular payments.

Closed-end credit: a type of installment loan in which the amount borrowed and the interest are repaid in a specified number of equal payments.

Open-end credit: a type of installment loan in which there is no fixed amount borrowed or fixed number of payments. Payments are made until the loan is paid off.

12-1 INSTALLMENT LOANS AND CLOSED-END CREDIT LEARNING OUTCOMES 1 Find the amount financed, the installment price, and the finance charge of an

installment loan. 2 Find the installment payment of an installment loan. 3 Find the estimated annual percentage rate (APR) using a table.

Should you or your business take out an installment loan? That depends on the interest you will pay and how it is computed. The interest associated with an installment loan is part of the charges referred to as finance charges or carrying charges. In addition to accrued interest charges, installment loans often include charges for insurance, credit-report fees, or loan fees. Under the truth-in-lending law, all of these charges must be disclosed in writing to the consumer.

1 Find the amount financed, the installment price, and the finance charge of an installment loan.

The cash price is the price you pay if you pay all at once at the time of the purchase. If you pay on an installment basis instead, the down payment is a partial payment of the cash price at the time of the purchase. The amount financed is the cash price minus the down payment. The installment payment is the amount you pay each period, including interest, to pay off the loan. The installment price is the total paid, including all of the installment payments, the finance charges, and the down payment.

Finance charges or carrying charges: the interest and any fee associated with an installment loan.

Cash price: the price if all charges are paid at once at the time of the purchase.

Down payment: a partial payment that is paid at the time of the purchase.

Amount financed: the cash price minus the down payment.

Installment payment: the amount that is paid (including interest) in each regular payment.

Installment price: the total amount paid for a purchase, including all payments, the finance charges, and the down payment.

HOW TO Find the amount financed and the installment price 1. Find the amount financed: Subtract the down payment from the cash price.

2. Find the installment price: Add the down payment to the total of the installment payments.

Installment price = total of installment payments + down payment

Amount financed = cash price - down payment

EXAMPLE 1 The 7th Inning purchased a mat cutter for the framing department on the installment plan with a $600 down payment and 12 payments of $145.58. Find the install- ment price of the mat cutter.

= $1,746.96 $145.58*12 =

Total of installment payments

= a number of installments

b * a installment payment

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The installment price is $2,346.96.

= $2,346.96 = $1,746.96 + $600

Installment price = total of installment payments + down payment

HOW TO Find the finance charge of an installment loan 1. Determine the cash price of the item. 2. Find the installment price of the item. 3. Subtract the result found in step 2 from the result of step 1.

Finance charge � installment price � cash price

EXAMPLE 2 If the cash price of the mat cutter in Example 1 was $2,200, find the finance charge and the amount financed.

The finance charge is $146.96 and the amount financed is $1,600.

= $1,600 = $2,200 - $600

Amount financed = cash price - down payment.

= $146.96 Down payment = $600 = $2,346.96 - $2,200.00 Cash price = $2,200.00 Finance charge = installment price - cash price Installment price = $2,346.96

2 Find the installment payment of an installment loan.

Since the installment price is the total of the installment payments plus the down payment, we can find the installment payment if we know the installment price, the down payment, and the number of payments.

HOW TO Find the installment payment, given the installment price, the downpayment, and the number of payments

1. Find the total of the installment payments: Subtract the down payment from the installment price.

2. Divide the total of the installment payments by the number of installment payments.

Installment payment = total of installment payments

number of payments

Total of installment payments = installment price - down payment

STOP AND CHECK 2. A copy machine is purchased on the installment plan with a

$200 down payment and 24 monthly payments of $118.50. The cash price is $2,695. Find the amount financed, installment price, and finance charge for the machine.

1. An ice machine with a cash price of $1,095 is purchased on the installment plan with a $100 down payment and 18 monthly payments of $62.50. Find the amount financed, installment price, and finance charge for the machine.

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3. An industrial freezer with a cash price of $2,295 is purchased on the installment plan with a $275 down payment and 30 monthly installment payments of $78.98. Find the amount financed, installment price, and finance charge for the freezer.

4. The cash price of a music system is $2,859 and the installment price is $3,115.35. How much is the finance charge?

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428 CHAPTER 12

3 Find the estimated annual percentage rate (APR) using a table.

In 1969 the federal government passed the Consumer Credit Protection Act, Regulation Z, also known as the Truth-in-Lending Act. Several amendments have been made to this original legis- lation. It requires that a lending institution tell the borrower, in writing, what the actual annual rate of interest is as it applies to the balance due on the loan each period. This interest rate tells the borrower the true cost of the loan.

If you borrowed $1,500 for a year and paid an interest charge of $165, you would be paying an interest rate of 11% annually on the entire $1,500 But if you paid the money back in 12 monthly installments of $138.75

you would not have the use of the $1,500 for a full year. Instead, you would be paying it back in 12 payments of $138.75 each. Thus, you are losing the use of some of the money every month but are still paying interest at the rate of 11% of the entire amount. This means that you are actually paying more than 11% interest. The equivalent rate is the annual percentage rate (APR). Applied to installment loans, the APR is the annual simple interest rate equivalent that is actually being paid on the unpaid balances. The APR can be determined using a government-is- sued table.

The federal government issues annual percentage rate tables, which are used to find APR rates (within which is the federal standard). A portion of one of these tables, based on the number of monthly payments, is shown in Table 12-1.

1 4%,

$138.75), , 12 =([$1,500 + $165]

(165 , $1,500 = 0.11 = 11%).

EXAMPLE 3 The installment price of a drafting table was $1,627 for a 12-month loan. If a $175 down payment had been made, find the installment payment.

The installment payment is $121.

= $1,452

12 = $121 Divide.

Installment payment = total of installment payments

number of payments

= $1,627 - $175 = $1,452 Subtract. Total of installment payments = installment price - down paymentProtect Your Credit Rating

Your credit reputation is just as important as your personal reputa- tion. Three different agencies track credit records. They are Equifax, Experian, and TransUnion. You are entitled to a free annual credit report from each of these three nationwide consumer reporting agencies.

TIP

STOP AND CHECK 2. The installment price of a piano is $8,997.40 and a down

payment of $1,000 is made. What is the monthly installment payment if the piano is financed for 36 months?

1. The installment price of a refrigerator is $2,087 for a 24-month loan. If a down payment of $150 had been made, what is the installment payment?

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3. The installment price of a tire machine is $2,795.28. A down payment of $600 is made. What is the installment payment if the machine is financed for 36 months?

4. Find the installment payment for a trailer if its installment price is $3,296.96 over 30 months and an $800 down payment is made.

HOW TO Find the estimated annual percentage rate using a per $100 of amount financed table 1. Find the interest per $100 of amount financed: Divide the finance charge including interest

by the amount financed and multiply by $100.

2. Find the row corresponding to the number of monthly payments. Move across the row to find the number closest to the value from step 1. Read up the column to find the annual percentage rate for that column. If the result in step 1 is exactly halfway between two table values, a rate halfway between the two rates can be used.

Interest per $100 = finance charge

amount financed * $100

Annual percentage rate (APR): the equivalent rate of an installment loan that is equivalent to an annual simple interest rate.

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TABLE 12-1 Interest per $100 of Amount Financed

Number APR (Annual Percentage Rate) for Selected Rates of monthly payments 10.75% 11.00% 11.25% 11.50% 11.75% 12.00% 12.25% 12.50% 12.75% 13.00% 13.25% 13.50% 13.75% 14.00% 14.25% 15.00%

1 0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.15 1.17 1.19 1.25 2 1.35 1.38 1.41 1.44 1.47 1.50 1.53 1.57 1.60 1.63 1.66 1.69 1.72 1.75 1.78 1.88 3 1.80 1.84 1.88 1.92 1.96 2.01 2.05 2.09 2.13 2.17 2.22 2.26 2.30 2.34 2.38 2.51 4 2.25 2.30 2.35 2.41 2.46 2.51 2.57 2.62 2.67 2.72 2.78 2.83 2.88 2.93 2.99 3.14 5 2.70 2.77 2.83 2.89 2.96 3.02 3.08 3.15 3.21 3.27 3.34 3.40 3.46 3.53 3.59 3.78 6 3.16 3.23 3.31 3.38 3.45 3.53 3.60 3.68 3.75 3.83 3.90 3.97 4.05 4.12 4.20 4.42 7 3.62 3.70 3.78 3.87 3.95 4.04 4.12 4.21 4.29 4.38 4.47 4.55 4.64 4.72 4.81 5.06 8 4.07 4.17 4.26 4.36 4.46 4.55 4.65 4.74 4.84 4.94 5.03 5.13 5.22 5.32 5.42 5.71 9 4.53 4.64 4.75 4.85 4.96 5.07 5.17 5.28 5.39 5.49 5.60 5.71 5.82 5.92 6.03 6.35

10 4.99 5.11 5.23 5.35 5.46 5.58 5.70 5.82 5.94 6.05 6.17 6.29 6.41 6.53 6.65 7.00 11 5.45 5.58 5.71 5.84 5.97 6.10 6.23 6.36 6.49 6.62 6.75 6.88 7.01 7.14 7.27 7.66 12 5.92 6.06 6.20 6.34 6.48 6.62 6.76 6.90 7.04 7.18 7.32 7.46 7.60 7.74 7.89 8.31 13 6.38 6.53 6.68 6.84 6.99 7.14 7.29 7.44 7.59 7.75 7.90 8.05 8.20 8.36 8.51 8.97 14 6.85 7.01 7.17 7.34 7.50 7.66 7.82 7.99 8.15 8.31 8.48 8.64 8.81 8.97 9.13 9.63 15 7.32 7.49 7.66 7.84 8.01 8.19 8.36 8.53 8.71 8.88 9.06 9.23 9.41 9.59 9.76 10.29 16 7.78 7.97 8.15 8.34 8.53 8.71 8.90 9.08 9.27 9.46 9.64 9.83 10.02 10.20 10.39 10.95 17 8.25 8.45 8.65 8.84 9.04 9.24 9.44 9.63 9.83 10.03 10.23 10.43 10.63 10.82 11.02 11.62 18 8.73 8.93 9.14 9.35 9.56 9.77 9.98 10.19 10.40 10.61 10.82 11.03 11.24 11.45 11.66 12.29 19 9.20 9.42 9.64 9.86 10.08 10.30 10.52 10.74 10.96 11.18 11.41 11.63 11.85 12.07 12.30 12.97 20 9.67 9.90 10.13 10.37 10.60 10.83 11.06 11.30 11.53 11.76 12.00 12.23 12.46 12.70 12.93 13.64 21 10.15 10.39 10.63 10.88 11.12 11.36 11.61 11.85 12.10 12.34 12.59 12.84 13.08 13.33 13.58 14.32 22 10.62 10.88 11.13 11.39 11.64 11.90 12.16 12.41 12.67 12.93 13.19 13.44 13.70 13.96 14.22 15.00 23 11.10 11.37 11.63 11.90 12.17 12.44 12.71 12.97 13.24 13.51 13.78 14.05 14.32 14.59 14.87 15.68 24 11.58 11.86 12.14 12.42 12.70 12.98 13.26 13.54 13.82 14.10 14.38 14.66 14.95 15.23 15.51 16.37 25 12.06 12.35 12.64 12.93 13.22 13.52 13.81 14.10 14.40 14.69 14.98 15.28 15.57 15.87 16.17 17.06 26 12.54 12.85 13.15 13.45 13.75 14.06 14.36 14.67 14.97 15.28 15.59 15.89 16.20 16.51 16.82 17.75 27 13.03 13.34 13.66 13.97 14.29 14.60 14.92 15.24 15.56 15.87 16.19 16.51 16.83 17.15 17.47 18.44 28 13.51 13.84 14.16 14.49 14.82 15.15 15.48 15.81 16.14 16.47 16.80 17.13 17.46 17.80 18.13 19.14 29 14.00 14.33 14.67 15.01 15.35 15.70 16.04 16.38 16.72 17.07 17.41 17.75 18.10 18.45 18.79 19.83 30 14.48 14.83 15.19 15.54 15.89 16.24 16.60 16.95 17.31 17.66 18.02 18.38 18.74 19.10 19.45 20.54 31 14.97 15.33 15.70 16.06 16.43 16.79 17.16 17.53 17.90 18.27 18.63 19.00 19.38 19.75 20.12 21.24 32 15.46 15.84 16.21 16.59 16.97 17.35 17.73 18.11 18.49 18.87 19.25 19.63 20.02 20.40 20.79 21.95 33 15.95 16.34 16.73 17.12 17.51 17.90 18.29 18.69 19.08 19.47 19.87 20.26 20.66 21.06 21.46 22.65 34 16.44 16.85 17.25 17.65 18.05 18.46 18.86 19.27 19.67 20.08 20.49 20.90 21.31 21.72 22.13 23.37 35 16.94 17.35 17.77 18.18 18.60 19.01 19.43 19.85 20.27 20.69 21.11 21.53 21.95 22.38 22.80 24.08 36 17.43 17.86 18.29 18.71 19.14 19.57 20.00 20.43 20.87 21.30 21.73 22.17 22.60 23.04 23.48 24.80 37 17.93 18.37 18.81 19.25 19.69 20.13 20.58 21.02 21.46 21.91 22.36 22.81 23.25 23.70 24.16 25.51 38 18.43 18.88 19.33 19.78 20.24 20.69 21.15 21.61 22.07 22.52 22.99 23.45 23.91 24.37 24.84 26.24 39 18.93 19.39 19.86 20.32 20.79 21.26 21.73 22.20 22.67 23.14 23.61 24.09 24.56 25.04 25.52 26.96 40 19.43 19.90 20.38 20.86 21.34 21.82 22.30 22.79 23.27 23.76 24.25 24.73 25.22 25.71 26.20 27.69 41 19.93 20.42 20.91 21.40 21.89 22.39 22.88 23.38 23.88 24.38 24.88 25.38 25.88 26.39 26.89 28.41 42 20.43 20.93 21.44 21.94 22.45 22.96 23.47 23.98 24.49 25.00 25.51 26.03 26.55 27.06 27.58 29.15 43 20.94 21.45 21.97 22.49 23.01 23.53 24.05 24.57 25.10 25.62 26.15 26.68 27.21 27.74 28.27 29.88 44 21.44 21.97 22.50 23.03 23.57 24.10 24.64 25.17 25.71 26.25 26.79 27.33 27.88 28.42 28.97 30.62 45 21.95 22.49 23.03 23.58 24.12 24.67 25.22 25.77 26.32 26.88 27.43 27.99 28.55 29.11 29.67 31.36 46 22.46 23.01 23.57 24.13 24.69 25.25 25.81 26.37 26.94 27.51 28.08 28.65 29.22 29.79 30.36 32.10 47 22.97 23.53 24.10 24.68 25.25 25.82 26.40 26.98 27.56 28.14 28.72 29.31 29.89 30.48 31.07 32.84 48 23.48 24.06 24.64 25.23 25.81 26.40 26.99 27.58 28.18 28.77 29.37 29.97 30.57 31.17 31.77 33.59 49 23.99 24.58 25.18 25.78 26.38 26.98 27.59 28.19 28.80 29.41 30.02 30.63 31.24 31.86 32.48 34.34 50 24.50 25.11 25.72 26.33 26.95 27.56 28.18 28.80 29.42 30.04 30.67 31.29 31.92 32.55 33.18 35.09 51 25.02 25.64 26.26 26.89 27.52 28.15 28.78 29.41 30.05 30.68 31.32 31.96 32.60 33.25 33.89 35.84 52 25.53 26.17 26.81 27.45 28.09 28.73 29.38 30.02 30.67 31.32 31.98 32.63 33.29 33.95 34.61 36.60 53 26.05 26.70 27.35 28.00 28.66 29.32 29.98 30.64 31.30 31.97 32.63 33.30 33.97 34.65 35.32 37.36 54 26.57 27.23 27.90 28.56 29.23 29.91 30.58 31.25 31.93 32.61 33.29 33.98 34.66 35.35 36.04 38.12 55 27.09 27.77 28.44 29.13 29.81 30.50 31.18 31.87 32.56 33.26 33.95 34.65 35.35 36.05 36.76 38.88 56 27.61 28.30 28.99 29.69 30.39 31.09 31.79 32.49 33.20 33.91 34.62 35.33 36.04 36.76 37.48 39.65 57 28.13 28.84 29.54 30.25 30.97 31.68 32.39 33.11 33.83 34.56 35.28 36.01 36.74 37.47 38.20 40.42 58 28.66 29.37 30.10 30.82 31.55 32.27 33.00 33.74 34.47 35.21 35.95 36.69 37.43 38.18 38.93 41.19 59 29.18 29.91 30.65 31.39 32.13 32.87 33.61 34.36 35.11 35.86 36.62 37.37 38.13 38.89 39.66 41.96 60 29.71 30.45 31.20 31.96 32.71 33.47 34.23 34.99 35.75 36.52 37.29 38.06 38.83 39.61 40.39 42.74

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Number APR (Annual Percentage Rate) for Selected Rates of monthly payments 15.50% 15.75% 16.00% 16.25% 16.50% 16.75% 17.00% 19.50% 19.75% 20.00% 20.25% 20.50% 20.75% 21.00% 21.25% 21.50%

1 1.29 1.31 1.33 1.35 1.37 1.40 1.42 1.62 1.65 1.67 1.69 1.71 1.73 1.75 1.77 1.79 2 1.94 1.97 2.00 2.04 2.07 2.10 2.13 2.44 2.48 2.51 2.54 2.57 2.60 2.63 2.66 2.70 3 2.59 2.64 2.68 2.72 2.76 2.80 2.85 3.27 3.31 3.35 3.39 3.44 3.48 3.52 3.56 3.60 4 3.25 3.30 3.36 3.41 3.46 3.51 3.57 4.10 4.15 4.20 4.25 4.31 4.36 4.41 4.47 4.52

TABLE 12-1 Interest per $100 of Amount Financed—Continued

5 3.91 3.97 4.04 4.10 4.16 4.23 4.29 4.93 4.99 5.06 5.12 5.18 5.25 5.31 5.37 5.44 6 4.57 4.64 4.72 4.79 4.87 4.94 5.02 5.76 5.84 5.91 5.99 6.06 6.14 6.21 6.29 6.36 7 5.23 5.32 5.40 5.49 5.58 5.66 5.75 6.60 6.69 6.78 6.86 6.95 7.04 7.12 7.21 7.29 8 5.90 6.00 6.09 6.19 6.29 6.38 6.48 7.45 7.55 7.64 7.74 7.84 7.94 8.03 8.13 8.23 9 6.57 6.68 6.78 6.89 7.00 7.11 7.22 8.30 8.41 8.52 8.63 8.73 8.84 8.95 9.06 9.17

10 7.24 7.36 7.48 7.60 7.72 7.84 7.96 9.15 9.27 9.39 9.51 9.63 9.75 9.88 10.00 10.12 11 7.92 8.05 8.18 8.31 8.44 8.57 8.70 10.01 10.14 10.28 10.41 10.54 10.67 10.80 10.94 11.07 12 8.59 8.74 8.88 9.02 9.16 9.30 9.45 10.87 11.02 11.16 11.31 11.45 11.59 11.74 11.88 12.02 13 9.27 9.43 9.58 9.73 9.89 10.04 10.20 11.74 11.90 12.05 12.21 12.36 12.52 12.67 12.83 12.99 14 9.96 10.12 10.29 10.45 10.67 10.78 10.95 12.61 12.78 12.95 13.11 13.28 13.45 13.62 13.79 13.95 15 10.64 10.82 11.00 11.17 11.35 11.53 11.71 13.49 13.67 13.85 14.03 14.21 14.39 14.57 14.75 14.93 16 11.33 11.52 11.71 11.90 12.09 12.28 12.46 14.37 14.56 14.75 14.94 15.13 15.33 15.52 15.71 15.90 17 12.02 12.22 12.42 12.62 12.83 13.03 13.23 15.25 15.46 15.66 15.86 16.07 16.27 16.48 16.68 16.89 18 12.72 12.93 13.14 13.35 13.57 13.78 13.99 16.14 16.36 16.57 16.79 17.01 17.22 17.44 17.66 17.88 19 13.41 13.64 13.86 14.09 14.31 14.54 14.76 17.03 17.26 17.49 17.72 17.95 18.18 18.41 18.64 18.87 20 14.11 14.35 14.59 14.82 15.06 15.30 15.54 17.93 18.17 18.41 18.66 18.90 19.14 19.38 19.63 19.87 21 14.82 15.06 15.31 15.56 15.81 16.06 16.31 18.83 19.09 19.34 19.60 19.85 20.11 20.36 20.62 20.87 22 15.52 15.78 16.04 16.30 16.57 16.83 17.09 19.74 20.01 20.27 20.54 20.81 21.08 21.34 21.61 21.88 23 16.23 16.50 16.78 17.05 17.32 17.60 17.88 20.65 20.93 21.21 21.49 21.77 22.05 22.33 22.61 22.90 24 16.94 17.22 17.51 17.80 18.09 18.37 18.66 21.56 21.86 22.15 22.44 22.74 23.03 23.33 23.62 23.92 25 17.65 17.95 18.25 18.55 18.85 19.15 19.45 22.48 22.79 23.10 23.40 23.71 24.02 24.32 24.63 24.94 26 18.37 18.68 18.99 19.30 19.62 19.93 20.24 23.41 23.73 24.04 24.36 24.68 25.01 25.33 25.65 25.97 27 19.09 19.41 19.74 20.06 20.39 20.71 21.04 24.33 24.67 25.00 25.33 25.67 26.00 26.34 26.67 27.01 28 19.81 20.15 20.48 20.82 21.16 21.50 21.84 25.27 25.61 25.96 26.30 26.65 27.00 27.35 27.70 28.05 29 20.53 20.88 21.23 21.58 21.94 22.29 22.64 26.20 26.56 26.92 27.28 27.64 28.00 28.37 28.73 29.09 30 21.26 21.62 21.99 22.35 22.72 23.08 23.45 27.14 27.52 27.89 28.26 28.64 29.01 29.39 29.77 30.14 31 21.99 22.37 22.74 23.12 23.50 23.88 24.26 28.09 28.47 28.86 29.25 29.64 30.03 30.42 30.81 31.20 32 22.72 23.11 23.50 23.89 24.28 24.68 25.07 29.04 29.44 29.84 30.24 30.64 31.05 31.45 31.85 32.26 33 23.46 23.86 24.26 24.67 25.07 25.48 25.88 29.99 30.40 30.82 31.23 31.65 32.07 32.49 32.91 33.33 34 24.19 24.61 25.03 25.44 25.86 26.28 26.70 30.95 31.37 31.80 32.23 32.67 33.10 33.53 33.96 34.40 35 24.94 25.36 25.79 26.23 26.66 27.09 27.52 31.91 32.35 32.79 33.24 33.68 34.13 34.58 35.03 35.47 36 25.68 26.12 26.57 27.01 27.46 27.90 28.35 32.87 33.33 33.79 34.25 34.71 35.17 35.63 36.09 36.56 37 26.42 26.88 27.34 27.80 28.26 28.72 29.18 33.84 34.32 34.79 35.26 35.74 36.21 36.69 37.16 37.64 38 27.17 27.64 28.11 28.59 29.06 29.53 30.01 34.82 35.30 35.79 36.28 36.77 37.26 37.75 38.24 38.73 39 27.92 28.41 28.89 29.38 29.87 30.36 30.85 35.80 36.30 36.80 37.30 37.81 38.31 38.82 39.32 39.83 40 28.68 29.18 29.68 30.18 30.68 31.18 31.68 36.78 37.29 37.81 38.33 38.85 39.37 39.89 40.41 40.93 41 29.44 29.95 30.46 30.97 31.49 32.01 32.52 37.77 38.30 38.83 39.36 39.89 40.43 40.96 41.50 42.04 42 30.19 30.72 31.25 31.78 32.31 32.84 33.37 38.76 39.30 39.85 40.40 40.95 41.50 42.05 42.60 43.15 43 30.96 31.50 32.04 32.58 33.13 33.67 34.22 39.75 40.31 40.87 41.44 42.00 42.57 43.13 43.70 44.27 44 31.72 32.28 32.83 33.39 33.95 34.51 35.07 40.75 41.33 41.90 42.48 43.06 43.64 44.22 44.81 45.39 45 32.49 33.06 33.63 34.20 34.77 35.35 35.92 41.75 42.35 42.94 43.53 44.13 44.72 45.32 45.92 46.52 46 33.26 33.84 34.43 35.01 35.60 36.19 36.78 42.76 43.37 43.98 44.58 45.20 45.81 46.42 47.03 47.65 47 34.03 34.63 35.23 35.83 36.43 37.04 37.64 43.77 44.40 45.02 45.64 46.27 46.90 47.53 48.16 48.79 48 34.81 35.42 36.03 36.65 37.27 37.88 38.50 44.79 45.43 46.07 46.71 47.35 47.99 48.64 49.28 49.93 49 35.59 36.21 36.84 37.47 38.10 38.74 39.37 45.81 46.46 47.12 47.77 48.43 49.09 49.75 50.41 51.08 50 36.37 37.01 37.65 38.30 38.94 39.59 40.24 46.83 47.50 48.17 48.84 49.52 50.19 50.87 51.55 52.23 51 37.15 37.81 38.46 39.12 39.79 40.45 41.11 47.86 48.55 49.23 49.92 50.61 51.30 51.99 52.69 53.38 52 37.94 38.61 39.28 39.96 40.63 41.31 41.99 48.89 49.59 50.30 51.00 51.71 52.41 53.12 53.83 54.55 53 38.72 39.41 40.10 40.79 41.48 42.17 42.87 49.93 50.65 51.37 52.09 52.81 53.53 54.26 54.98 55.71 54 39.52 40.22 40.92 41.63 42.33 43.04 43.75 50.97 51.70 52.44 53.17 53.91 54.65 55.39 56.14 56.88 55 40.31 41.03 41.74 42.47 43.19 43.91 44.64 52.02 52.76 53.52 54.27 55.02 55.78 56.54 57.30 58.06 56 41.11 41.84 42.57 43.31 44.05 44.79 45.53 53.06 53.83 54.60 55.37 56.14 56.91 57.68 58.46 59.24 57 41.91 42.65 43.40 44.15 44.91 45.66 46.42 54.12 54.90 55.68 56.47 57.25 58.04 58.84 59.63 60.43 58 42.71 43.47 44.23 45.00 45.77 46.54 47.32 55.17 55.97 56.77 57.57 58.38 59.18 59.99 60.80 61.62 59 43.51 44.29 45.07 45.85 46.64 47.42 48.21 56.23 57.05 57.87 58.68 59.51 60.33 61.15 61.98 62.81 60 44.32 45.11 45.91 46.71 47.51 48.31 49.12 57.30 58.13 58.96 59.80 60.64 61.48 62.32 63.17 64.01

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EXAMPLE 4 Lewis Strang bought a motorcycle for $3,500, which was financed at $142 per month for 24 months. The down payment was $500. Find the APR.

Find the row for 24 monthly payments. Move across to find the number nearest to $13.60.

Find the table value closest to $13.60.

Move up to the top of that column to find the annual percentage rate, which is 12.5%.

$13.82

- 13.60 $ 0.22

$13.60 - $13.54

$ 0.06 Closest

value

Interest per $100 = finance charge

amount financed * $100 =

$408

$3,000 ($100) = $13.60

Amount financed = $3,500 - $500 = $3,000 Finance charge = $3,908 - $3,500 = $408

Installment price = 24($142) + $500 = $3,408 + $500 = $3,908

TIP Finding the Closest Table Value

Another way to find the closest table value to the interest per $100 is to compare the interest to the amount halfway between two table values. The halfway amount is the average of the two table values.

In the previous example, $13.60 is between $13.54 and $13.82.

Because $13.60 is less than the halfway amount ($13.68), it is closer to the lower table value ($13.54).

= $13.68

Halfway = $13.54 + $13.82

2 =

$27.36

Halfway = larger value + smaller value

Not All Quoted APRs Are the Same! The APR quoted on a loan may or may not include other fees and charges associated with a loan such as private mortgage insurance, processing fees, and discount points. Some do, some don’t. Look closely at the details.

DID YOU KNOW?

12-1 SECTION EXERCISES SKILL BUILDERS 1. Find the installment price of a recliner bought on the

installment plan with a down payment of $100 and six payments of $108.20.

2. Find the amount financed if a $125 down payment is made on a TV with a cash price of $579.

STOP AND CHECK 2. Peggy Portzen purchased new kitchen appliances with a

cash price of $6,800. After making a down payment of $900, she financed the balance over 24 months with payments of $279.65. Find the annual percentage rate (APR) of the loan.

1. Jaime Lopez purchased a preowned car that listed for $11,935. After making a down payment of $1,500, he financed the balance over 36 months with payments of $347.49 per month. Use Table 12-1 to find the annual percentage rate (APR) of the loan.

�

3. Alan Dan could purchase a jet ski for $9,995 cash. He paid $2,000 down and financed the balance with 36 monthly payments of $295.34. Find the APR of the loan.

4. Nellie Chapman bought a Harley-Davidson motorcycle that had a cash price of $12,799 with a $2,500 down payment. She paid for the motorcycle in 48 monthly payments of $296.37. Find the APR for the loan.

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3. Stephen Helba purchased a TV with surround sound and remote control on an installment plan with $100 down and 12 payments of $106.32. Find the installment price of the TV.

4. A queen-size bedroom suite can be purchased on an installment plan with 18 payments of $97.42 if an $80 down payment is made. What is the installment price of the suite?

5. Zack’s Trailer Sales will finance a 16-foot utility trailer with ramps and electric brakes. If a down payment of $100 and eight monthly payments of $82.56 are required, what is the installment price of the trailer?

6. A forklift is purchased for $10,000. The forklift is used as collateral and no down payment is required. Twenty-four monthly payments of $503 are required to repay the loan. What is the installment price of the forklift?

7. A computer with software costs $2,987, and Docie Johnson has agreed to pay a 19% per year finance charge on the cash price. If she contracts to pay the loan in 18 months, how much will she pay each month?

8. The cash price of a bedroom suite is $2,590. There is a 24% finance charge on the cash price and 12 monthly payments. Find the monthly payment.

9. Find the monthly payment on a HD LED television with an installment price of $929, 12 monthly payments, and a down payment of $100.

10. The installment price of a teakwood extension table and four chairs is $625 with 18 monthly payments and a down payment of $75. What is the monthly payment?

11. An entertainment center is financed at a total cost of $2,357 including a down payment of $250. If the center is financed over 24 months, find the monthly payment.

12. A Hepplewhite sofa costs $3,780 in cash. Jaquanna Wilson will purchase the sofa in 36 monthly installment payments. A 13% per year finance charge will be assessed on the amount financed. Find the finance charge, the installment price, and the monthly payment.

APPLICATIONS

13. A fishing boat is purchased for $5,600 and financed for 36 months. If the total finance charge is $1,025, find the annual percentage rate using Table 12-1.

14. An air compressor costs $780 and is financed with monthly payments for 12 months. The total finance charge is $90. Find the annual percentage rate using Table 12-1.

15. Jim Meriweather purchased an engraving machine for $28,000 and financed it for 36 months. The total finance charge was $5,036. Use Table 12-1 to find the annual percentage rate.

12-2 PAYING A LOAN BEFORE IT IS DUE: THE RULE OF 78 LEARNING OUTCOME 1 Find the interest refund using the rule of 78.

If a closed-end installment loan is paid entirely before the last payment is actually due, is part of the interest refundable? In most cases it is, but not always at the rate you might hope. If you paid a 12-month loan in 6 months, you might expect a refund of half the total interest. However, this

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Rule of 78: method for determining the amount of refund of the finance charge for an installment loan that is paid before it is due.

Refund fraction: the fractional part of the total interest that is refunded when a loan is paid early using the rule of 78.

of the loan. The interest for the second payment is based on of the amount financed because 112 11 12

12 12 of this amount has already been paid. The interest for the third payment is of the amount1012 financed, and so on. The interest on the last payment is based on of the amount financed.

The sum of all the parts accruing interest for a 12-month loan is or 78.

Thus, 78 equal parts accrue interest. The interest each part accrues is the same because the rate is the same and the parts are the same (each is of the principal). Because 78 equal parts112

7 + 6 + 5 + 4 + 3 + 2 + 1, 12 + 11 + 10 + 9 + 8 +

1 12

each accrue equal interest, the interest each part accrues must be of the total interest for the one-year loan. So if the loan is paid in full with three months remaining, then the interest that would have accrued in the 10th, 11th, and 12th months is refunded. In the 10th month, three parts each accrue of the total interest; in the 11th month, two parts each accrue of the total inter-178

1 78

est; and in the 12th month, one part accrues of the total interest. So each of the 3 + 2 + 1178 parts, or 6 parts, accrues of the total interest. Thus of the total interest is refunded. The frac-678

1 78

tion is called the refund fraction. Not all installment loans are for 12 months, but the rule of 78 gives us a pattern that we can

apply to loans of any allowable length.

6 78

HOW TO Find the refund fraction for the interest refund 1. The numerator is the sum of the digits from 1 through the number of months remaining of a

loan paid off before it was due. 2. The denominator is the sum of the digits from 1 through the original number of months of

the loan. 3. The original fraction, the reduced fraction, or the decimal equivalent of the fraction can be used.

The sum-of-digits table in Table 12-2 can be used to find the numerator and denominator of the refund fraction.

TABLE 12-2 Sum-of-Digits

Months Sum of digits 1 1 2 3 3 6 4 10 5 15 6 21 7 28 8 36 9 45

10 55 11 66 12 78 13 91 14 105 15 120 16 136 17 153 18 171 19 190 20 210

Months Sum of digits 21 231 22 253 23 276 24 300 25 325 26 351 27 378 28 406 29 435 30 465 31 496 32 528 33 561 34 595 35 630 36 666 37 703 38 741 39 780 40 820

Months Sum of digits 41 861 42 903 43 946 44 990 45 1,035 46 1,081 47 1,128 48 1,176 49 1,225 50 1,275 51 1,326 52 1,378 53 1,431 54 1,485 55 1,540 56 1,596 57 1,653 58 1,711 59 1,770 60 1,830

is not the case because the portion of the monthly payment that is interest is not the same from month to month. In some cases, interest or finance charge refunds are made according to the rule of 78. Some states allow this method to be used for short-term loans, generally 60 months or less. Laws and court rulings protect and inform the consumer in matters involving interest.

1 Find the interest refund using the rule of 78.

The rule of 78 is not based on the actual unpaid balance after a payment is made. Instead, it is an approximation that assumes the amount financed (which includes the interest) of a one-year loan is paid in 12 equal parts. For the first payment, the interest is based on the total amount financed, or

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There is a shortcut for finding the sum of consecutive numbers beginning with 1. You may be interested to know that a young boy in elementary school discovered this shortcut in the late 18th century. He later went on to be one of the greatest mathematicians of all time. His name was Carl Friedrich Gauss (1777–1855).

TIP The Sum of Consecutive Numbers Beginning with 1

Multiply the largest number by 1 more than the largest number and divide the product by 2.

Sum of consecutive numbers from 1 through 12 = 12(13)

2 =

156

2 = 78

Sum of consecutive numbers from 1 through 4 = 4(5)

2 =

2 = 10

Sum of consecutive numbers beginning with 1 = largest number * (largest number + 1)

TIP Continuous Sequence of Steps Using a Calculator

It is advisable in making calculations as in Example 2 that you use a continuous sequence of steps in a calculator. It is time-consuming and more mistakes are made if you reenter the result of a previous calculation to make another calculation.

For Example 2, the continuous sequence of steps is:

When using a calculator, there is no need to reduce fractions first.

CLEAR 117 * 10 , 78 = Q 15

HOW TO Find the interest refund using the rule of 78 1. Find the refund fraction. 2. Multiply the total interest by the refund fraction.

Interest refund = total interest * refund fraction

EXAMPLE 1 A loan for 12 months with interest of $117 is paid in full with four payments remaining. Find the refund fraction for the interest refund.

= 10

78 =

39 or 0.1282051282

= 1 + 2 + 3 + 4

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Refund fraction = sum of the digits for number of payments remaining

sum of the digits for total number of payments

10 , 78 = 0.1282051282

The refund fraction is or or 0.1282051282.539 10 78

EXAMPLE 2 Find the interest refund for the installment loan in Example 1.

= $15 = $117(0.1282051282)

Interest refund = total interest * refund fraction Total interest

Refund fraction or or 0.1282051282

Multiply.

39 =

= $117

The interest refund is $15.

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EXAMPLE 3 A loan for 36 months, with a finance charge of $1,276.50, is paid in full with 15 payments remaining. Find the finance charge to be refunded.

Calculator sequence: 1276.50 * 120 , 666 = = $230

= $1,276.50a120 666

b Finance charge refund = finance charge * refund fraction

Refund fraction = 120

666

= sum of digits from 1 through 15

sum of digits from 1 through 36

Refund fraction = sum of the digits for number of payments remaining

sum of the digits for total number of payments

36 * 37 , 2 = Q 666 15 * 16 , 2 = Q 120

The finance charge refund is $230.

STOP AND CHECK 2. A loan for 48 months has interest of $2,896 and is paid in

full with 18 months remaining. What is the refund fraction for the interest refund?

1. A loan for 12 months with interest of $397.85 is paid in full with five payments remaining. What is the refund fraction for the interest refund?

�

3. A loan for 36 months requires $1,798 interest. The loan is paid in full with 6 months remaining. How much interest is refunded?

4. Ruth Brechner borrowed money to purchase a retail business. The 60-month loan had $4,917 interest. Ruth’s business flourished and she repaid the loan after 50 months. How much interest refund did she receive?

12-2 SECTION EXERCISES SKILL BUILDERS 1. Calculate the refund fraction for a 60-month loan that is

paid off with 18 months remaining.

2. Find the refund fraction on an 18-month loan if it is paid off with 8 months remaining.

3. Find the interest refund on a 36-month loan with interest of $2,817 if the loan is paid in full with 9 months remaining.

4. Stephen Helba took out a loan to purchase a computer. He originally agreed to pay off the loan in 18 months with a finance charge of $205. He paid the loan in full after 12 payments. How much finance charge refund should he get?

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APPLICATIONS 5. John Paszel took out a loan for 48 months but paid it in full

after 28 months. Find the refund fraction he should use to calculate the amount of his refund.

6. If the finance charge on a loan made by Marjorie Young is $1,645 and the loan is to be paid in 48 monthly payments, find the finance charge refund if the loan is paid in full with 28 months remaining.

7. Phillamone Berry has a car loan with a company that refunds interest using the rule of 78 when loans are paid in full ahead of schedule. He is using an employee bonus to pay off his Traverse, which is on a 42-month loan. The total interest for the loan is $2,397, and he has 15 more payments to make. How much finance charge will he get credit for if he pays the loan in full immediately?

8. Dwayne Moody purchased a four-wheel drive vehicle and is using severance pay from his current job to pay off the vehicle loan before moving to his new job. The total interest on the 36-month loan is $3,227. How much finance charge refund will he receive if he pays the loan in full with 10 more payments left?

12-3 OPEN-END CREDIT LEARNING OUTCOMES 1. Find the finance charge and new balance using the average daily balance method. 2. Find the finance charge and new balance using the unpaid or previous month’s balance.

Open-end loans are often called line-of-credit accounts. While a person or company is paying off loans, that person or company may also be adding to the total loan account by making a new purchase or otherwise borrowing money on the account.

For example, you may want to use your Visa card to buy new textbooks even though you still owe for clothes bought last winter. Likewise, a business may use an open-end credit account to buy a new machine this month even though it still owes the bank for funds used to pay a major supplier six months ago.

Nearly all open-end accounts are billed monthly. Interest rates are most often stated as an- nual rates. The Fair Credit and Charge Card Disclosure Act of 1988 and updates passed since that time specify the required details that must be disclosed for charge cards and line-of-credit accounts. These details include all fees, grace period, how finance charges are calculated, how late fees are assessed, and so on. While this act addresses the disclosure of fees and charges, The Credit Card Act of 2009 (effective February 22, 2010) imposes regulations on credit card issuers in an attempt to stop them from unfairly taking advantage of consumers.

1 Find the finance charge and new balance using the average daily balance method.

Many lenders determine the finance charge using the average daily balance method. In this method, the daily balances of the account are determined, and then the sum of these balances is divided by the number of days in the billing cycle. This average daily balance is next multiplied by the monthly interest rate to find the finance charge for the month.

Even though open-end credit accounts are billed monthly, the monthly period may not coin- cide with the first and last days of a calendar month. To spread out the workload for the billing department, each account is given a monthly billing cycle. The billing cycle is the days that are included on a statement or bill. This cycle can start on any day of a month. For example, a billing cycle may start on the 22nd of one month and end on the 21st of the next month. This means that the number of days of a billing cycle will vary from month to month based on the number of days in the months involved.

Line-of-credit accounts: a type of open-end loan.

Average daily balance: the average of the daily balances for each day of the billing cycle.

Billing cycle: the days that are included on a statement or bill.

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HOW TO Find the average daily balance 1. Find the daily unpaid balance for each day in the billing cycle.

(a) Find the total purchases and cash advances charged to the account during the day. (b) Find the total credits (payments and adjustments) credited to the account during the day. (c) To the previous daily unpaid balance, add the total purchases and cash advances for the

day (from step 1a). Then subtract the total credits for the day (from step 1b).

2. Add the unpaid balances from step 1 for each day of the billing cycle, and divide the sum by the number of days in the cycle.

Average daily balance = sum of daily unpaid balances

number of days in billing cycle

Daily unpaid balance = previous daily unpaid balance + total purchases and cash advances for the day - total credits for the day

HOW TO Find the finance charge using the average daily balance 1. Determine the decimal equivalent of the rate per period. 2. Multiply the average daily balance by the decimal equivalent of the rate per period.

EXAMPLE 1 Use the chart showing May activity in the Hodge’s Tax Service charge account to determine the average daily balance and finance charge for the month. The bank’s finance charge is 1.5% per month on the average daily balance.

Date transaction posted Transaction Transaction amount May 1 Billing date Balance $122.70 May 7 Payment 25.00 May 10 Purchase (pencils) 12.00 May 13 Purchase (envelopes) 20.00 May 20 Cash advance 50.00 May 23 Purchase (business forms) 100.00

To find the average daily balance, we must find the unpaid balance for each day, add these bal- ances, and divide by the number of days.

Day Balance 1 122.70 2 122.70 3 122.70 4 122.70 5 122.70 6 122.70 7 97.70 8 97.70 9 97.70

10 109.70 (97.70 + 12)

(122.70 - 25)

Day Balance 11 109.70 12 109.70 13 129.70 14 129.70 15 129.70 16 129.70 17 129.70 18 129.70 19 129.70 20 179.70 (129.70 + 50)

(109.70 + 20)

Day Balance 21 179.70 22 179.70 23 279.70 24 279.70 25 279.70 26 279.70 27 279.70 28 279.70 29 279.70 30 279.70 31 279.70

(179.70 + 100)

The average daily balance can also be determined by grouping days that have the same balance. For the first six days, May 1–May 6, there is no activity, so the daily unpaid balance is the pre-

vious unpaid balance of $122.70. The sum of daily unpaid balances for these six days, then, is

On May 7 there is a payment of $25, which reduces the daily unpaid balance.

The new balance of $97.70 holds for the three days (May 7, 8, and 9) until May 10.

$97.70(3) = $293.10

$122.70 - $25 = $97.70

$122.70(6) = $736.20

122.70(6).

Total: $5,322.70 Average Daily Balance: $171.70

When Does the Balance Change?

In most cases, if a transaction reaches a financial institution at any time during the day, the transaction is posted and the balance is updated at the end of the business day. Thus, the new balance takes effect at the beginning of the next day. Calculations on the day’s unpaid balance are made on the end-of- day amount (same as beginning of next day).

TIP

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438 CHAPTER 12

Divide the sum of $5,322.70 by the 31 days.

To find the interest, multiply the average daily balance by the monthly interest rate of 1.5%.

The average daily balance is $171.70 and the finance charge is $2.58.

= $2.58 Finance charge = $171.70(0.015)

= $5,322.70

31 = $171.70

Average daily balance = sum of daily unpaid balances

number of days

Continue doing this until you get to the end of the cycle. The calculations can be organized in a chart.

Daily unpaid Number Date Change balance of days Partial sum May 1–May 6 $122.70 6 $ 736.20 May 7–May 9 -$25.00 97.70 3 293.10 May 10–May 12 +10.00 109.70 3 329.10 May 13–May 19 +20.00 129.70 7 907.90 May 20–May 22 +50.00 179.70 3 539.10 May 23–May 31 +100.00 279.70 9 2,517.30

Total 31 $5,322.70

STOP AND CHECK� Account Number Credit Limit Available Credit Billing Period

xxxx-xxxx-xxxx-xxxx $5,000 $4,212.28 9/24/12 to 10/24/12 Posting

Date Transaction

Date Description Amount

CR–Credit PY–Payment

9/26

10/6

10/8

10/10

10/14

10/20

9/24

10/02

10/06

10/10

10/12

10/16

10/19

The Store Oxford MS

Chili's Oxford MS

Durall St Cloud FL

Payment Received–Thank You

Foley's Knitwear San Antonio TX

Red Lobster Tupelo MS

JC Penny Co Oxford MS

$11.93

$15.24

$86.98

$927.86

$113.19

$22.88

$47.36

Finance Charge Balance

Average Daily

Balance

Monthly Periodic

Rate

Corresponding Annual

Percentage Rate

Finance Charge

Purchases

1.0750%

Variable

12.90%

Variable

12.90%

Cash Advances

$0.00

Previous Balance

Purchases

Other Charges

Cash Advances

Credits

Payments

Late Charges

Finance Charges

New Balance

–

1,406.54

297.58

.00

0.00

.00

927.86

.00

11.46

787.72

FIGURE 12-1

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2 Find the finance charge and new balance using the unpaid or previous month’s balance.

Not all open-end credit accounts use the average daily balance method for determining the monthly finance charge. Another method uses the unpaid or previous month’s balance as the basis for determining the finance charge. In this method, the new purchases or payments made during a month do not affect the finance charge for that month.

Use the statement in Figure 12-1 for Exercises 1–4.

1. Make a table showing the unpaid balance for each day in the billing period.

2. Find the average daily balance for the month.

3. Find the finance charge for the month. 4. Find the new balance for the month.

HOW TO Find the finance charge and new balance using the unpaid orprevious month’s balance Finance charge:

1. Find the monthly rate.

2. Multiply the unpaid or previous month’s balance by the monthly rate.

New balance:

1. Total the purchases and cash advances for the billing cycle. 2. Total the payments and credits for the billing cycle. 3. Adjust the unpaid balance of the previous month using the totals in steps 1 and 2.

New balance � Previous balance � Finance charge � Purchases and cash advances � Payments and credits

Finance charge = Unpaid balance * Monthly rate

Monthly rate = Annual percentage rate

EXAMPLE 2 Hanna Stein has a department store revolving credit account with an annual percentage rate of 21%. Her unpaid balance for her March billing cycle is $285.45. During the billing cycle she purchased shoes for $62.58 and a handbag for $35.18. She returned a blouse that she had purchased in the previous billing cycle, received a credit of $22.79, and she made a payment of $75. If the store uses the unpaid balance method, what are the finance charge and the new balance?IS

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Monthly rate:

Finance charge:

New balance:

New balance Previous balance Finance charge Purchases and cash advances Payments and credits

New balance = $285.45 + $5 + $97.76 - $97.79 = $290.42

-++= Total payments and credits = $75 + $22.79 = $97.79 Total purchases and cash advances = $62.58 + $35.18 = $97.76

Finance charge = $285.45(0.0175) = $5.00 Rounded from $4.995375Finance charge = Unpaid balance * Monthly rate Monthly rate =

21%

12 =

0.21

12 = 0.0175

Monthly rate = Annual percentage rate

STOP AND CHECK 2. Shameka Brown has a Best Buy Stores revolving credit

account that has an annual percentage rate of 15% on the unpaid balance. Her unpaid balance for the October billing cycle is $2,531.77. During the billing cycle, Shameka purchased movies for $58.63 and received $70 in cash. She purchased a camera for $562.78 and returned a printer purchased in September for credit of $85.46. Shameka made a payment of $455. Find the finance charge and new balance if Best Buy uses the unpaid balance method.

1. Shakina Brewster has a Target revolving credit account that has an annual percentage rate of 18% on the unpaid balance. Her unpaid balance for the July billing cycle is $1,285.96. During the billing cycle, Shakina purchased groceries for $98.76 and received $50 in cash. She purchased linens for $46.98. Shakina made a payment of $135. Find the finance charge and new balance if Target uses the unpaid balance method.

�

3. Dallas Hunsucker has a Master Card account with an annual percentage rate of 24%. The unpaid balance for his January billing cycle is $2,094.54. During the billing cycle he made grocery purchases of $65.82, $83.92, $12.73, and gasoline purchases of $29.12 and $28.87. He made a payment of $400. If the account applies the unpaid balance method, what were the finance charge and the new balance?

4. Ryan Bradley has a Visa Card with an introductory annual percentage rate of 9%. The unpaid balance for his February billing cycle is $245.18. During the billing cycle he purchased fresh flowers for $45.00, candy for $22.38, and gasoline for $36.53. He made a payment of $100 and had a return for credit of $74.93. If the account applies the unpaid balance method, what are the finance charge and the new balance?

12-3 SECTION EXERCISES SKILL BUILDERS 1. What is the monthly interest rate if an annual rate is 13.8%? 2. Find the monthly interest rate if the annual rate is 15.6%.

3. A credit card has an average daily balance of $2,817.48 and the monthly periodic rate is 1.325%. What is the finance charge for the month?

4. What is the finance charge on a credit card account that has an average daily balance of $5,826.42 and the monthly interest rate is 1.55%?

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APPLICATIONS 5. Jim Riddle has a credit card that charges 10% annual

interest on the monthly average daily balance for the billing cycle. The current billing cycle has 29 days. For 15 days his balance was $2,534.95. For 7 days the balance was $1,534.95. And for 7 days the balance was $1,892.57. Find the average daily balance. Find the amount of interest.

6. Suppose the charge account of Strong’s Mailing Service at the local supply store had a 1.8% interest rate per month on the average daily balance. Find the average daily balance if Strong’s had an unpaid balance on March 1 of $128.50, a payment of $20 posted on March 6, and a purchase of $25.60 posted on March 20. The billing cycle ends March 31.

7. Using Exercise 6, find Strong’s finance charge on April 1. 8. Make a chart to show the transactions for Rick Schiendler’s credit card account in which interest is charged on the average daily balance. The cycle begins on May 4, and the cycle ends on June 3. The beginning balance is $283.57. A payment of $200 is posted on May 18. A charge of $19.73 is posted on May 7. A charge of $53.82 is posted on May 12. A charge of $115.18 is posted on May 29. How many days are in the cycle? What is the average daily balance?

9. Rick is charged 1.42% per period. What is the finance charge for the cycle?

10. What is the beginning balance for the next cycle of Rick’s credit card account?

11. Jamel Cisco has a Visa Card with an annual percentage rate of 16.8%. The unpaid balance for his June billing cycle is $1,300.84. During the billing cycle he purchased a printer cartridge for $42.39, books for $286.50 and gasoline for $16.71. He made a payment of $1,200. If the account applies the unpaid balance method, what are the finance charge and the new balance?

12. Chaundra Mixon has a Master Card with an annual percentage rate of 19.8%. The unpaid balance for her August billing cycle is $675.21. During the billing cycle she purchased shoes for $87.52, a suit for $132.48, and a wallet for $28.94. She made a payment of $225. If the account applies the unpaid balance method, what are the finance charge and the new balance?

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Learning Outcomes Section 12-1

1 Find the amount financed, the installment price, and the finance charge of an installment loan. (p. 426)

SUMMARY CHAPTER 12

What to Remember with Examples

1. Find the amount financed: Subtract the down payment from the cash price.

2. Find the installment price: Add the down payment to the total of the installment payments.

Installment price = total of installment payments + down payment

Amount financed = cash price - down payment

Find the installment price of a computer that is paid for in 24 monthly payments of $113 if a down payment of $50 is made.

(24)($113) + $50 = $2,712 + $50 = $2,762

Find the finance charge of an installment loan:

Subtract the cash price from the installment price.

Finance charge = installment price - cash price

If the cash price of the computer in the previous example was $2,499, how much is the finance charge?

$2,762 - $2,499 = $263

2 Find the installment payment ofan installment loan. (p. 427) 1. Find the total of the installment payments: Subtract the down payment from the installmentprice.

2. Divide the total of installment payments by the number of installment payments.

Installment payment = total of installment payments

number of payments

Total of installment payments = installment price - down payment

Find the monthly payment on a computer if the cash price is $3,285. A 14% interest rate is charged on the cash price, and there are 12 monthly payments.

A computer has an installment price of $2,187.25 when financed over 18 months. If a $100 down payment is made, find the monthly payment.

Monthly payment = $2,087.25

18 = $115.96

$2,187.25 - $100 = $2,087.25

Monthly payment = $3,744.90

12 = $312.08

Installment price = $3,285 + $459.90 = $3,744.90 $3,285(0.14)(1) = $459.90

3 Find the estimated annual percentage rate (APR) using a table. (p. 428)

1. Find the interest per $100 of amount financed: Divide the finance charge by the amount financed and multiply by $100.

Interest per $100 = total finance charge

amount financed * $100

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Find the annual percentage rate on a loan of $500 that is repaid in 36 monthly installments. The interest for the loan is $95.

In the row for 36 months, move across to 19.14 (nearest to 19). APR is at the top of the column, 11.75%.

Interest per $100 = $95

$500 ($100) = $19

Section 12-2

1 Find the interest refund using therule of 78. (p. 433) Find the refund fraction.

1. The numerator is the sum of the digits from 1 through the number of months remaining of a loan paid off before it was due.

2. The denominator is the sum of the digits from 1 through the original number of months of the loan.

3. The original fraction, the reduced fraction or the decimal equivalent of the fraction can be used.

Find the refund fraction on a loan that has a total finance charge of $892 and was made for 24 months. The loan is paid in full with 10 months (payments) remaining.

= 55

300 or

60 or 0.1833333333

= sum of 1 to 10

sum of 1 to 24

Refund fraction = sum of digits from 1 to the number of periods remaining

sum of digits from 1 through original number of periods

Find the interest refund using the rule of 78.

1. Find the refund fraction. 2. Multiply the total interest by the refund fraction.

Interest refund = total interest * refund fraction

Find the interest refund for the previous example.

Interest refund = $892a11 60

b = $163.53 892 * 11 , 60 = Q 163.5333333

1. Find the daily unpaid balance for each day in the billing cycle. (a) Find the total purchases and cash advances charged to the account during the day. (b) Find the total credits (payments and adjustments) credited to the account during the day. (c) To the previous daily unpaid balance, add the total purchases and cash advances for the

day (from step 1a). Then subtract the total payments for the day (from step 1b).

2. Add the unpaid balances from step 1 for each day of the billing cycle, and divide the sum by the number of days in the cycle.

Average daily balance = sum of daily unpaid balances

number of days in billing cycle

and cash advances for the day - total credits for the day Daily unpaid balance = previous daily unpaid balance + total purchases

Section 12-3

1 Find the finance charge and newbalance using the average daily balance method. (p. 436)

2. Find the row corresponding to the number of monthly payments. Move across the row to find the number closest to the value from step 1. Read up the column to find the annual percentage rate for that column. If the result in step 1 is exactly half way between two table values use the higher rate or a rate half way between the two rates can be used.

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A credit card has a balance of $398.42 on September 14, the first day of the billing cycle. A charge of $182.37 is posted to the account on September 16. Another charge of $82.21 is posted to the account on September 25. The amount of a returned item ($19.98) is posted to the account on October 10 and a payment of $500 is made on October 12. The billing period ends on October 13. Find the average daily balance.

Find the finance charge using the average daily balance:

1. Determine the decimal equivalent of the rate per period. 2. Multiply the average daily balance by the decimal equivalent of the rate per period.

Find the finance charge for the average daily balance in the preceding example if the monthly rate is 1.3%.

Finance charge = $584.70(0.013) = $7.60

Finance charge:

1. Find the monthly rate.

2. Multiply the unpaid or previous month’s balance by the monthly rate.

New balance:

New balance previous balance finance charge purchases and cash advances payments and credits-

++=

Finance charge = Unpaid balance * Monthly rate

Monthly rate = Annual percentage rate

2 Find the finance charge and newbalance using the unpaid or previous month’s balance. (p. 439)

Dakota Beasley has a Visa account with an annual percentage rate of 24%. Her unpaid bal- ance for her September billing cycle is $381.15. During the billing cycle she made gasoline purchases of $25.18, $18.29, $22.75, and $19.12. She made a payment of $100. If the ac- count applies the unpaid balance method, what is the finance charge and the new balance?

= $374.11 New balance = $381.15 + $7.62 + $85.34 - $100

Payments = $100 = $85.34

Total purchases = $25.18 + $18.29 + $22.75 + $19.12 Finance charge = $381.15(0.02) = $7.62 Rounded from $7.623 Finance charge = Unpaid balance * Monthly rate

Monthly rate = 24%

12 =

0.24

12 = 0.02

Monthly rate = Annual percentage rate

Daily Unpaid Number Date Change Balance of Days Partial Sum September 14–15 $398.42 2 days $ 796.84 September 16–24 +$182.37 580.79 9 days 5,227.11 September 25–October 9 +82.21 663.00 15 days 9,945.00 October 10–11 -19.98 643.02 2 days 1,286.04 October 12–13 -500.00 143.02

Total 30 days $17,541.03 286.04 2 days

Average daily balance = $17,541.03 , 30 = $584.70

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NAME DATE

EXERCISES SET A CHAPTER 12

1. Find the installment price of a notebook computer system bought on the installment plan with $250 down and 12 pay- ments of $111.33.

2. Find the monthly payment on a water bed if the installment price is $1,050, the down payment is $200, and there are 10 monthly payments.

3. If the cash price of a refrigerator is $879 and a down payment of $150 is made, how much is to be financed?

4. Find the refund fraction for a 60-month loan if it is paid in full with 22 months remaining.

Use the rule of 78 to find the finance charge (interest) refund in each of the following.

Finance Number of Remaining Interest charge monthly payments payments refund

5. $238 12 4

6. $2,175 24 10

7. $896 18 4

EXCEL

8. The finance charge on a copier was $1,778. The loan for the copier was to be paid in 18 monthly payments. Find the fi- nance charge refund if it is paid off in eight months.

9. Becky Whitehead has a loan with $1,115 in finance charges, which she paid in full after 10 of the 24 monthly payments. What is her finance charge refund?

10. Alice Dubois was charged $455 in finance charges on a loan for 15 months. Find the finance charge refund if she pays off the loan in full after 10 payments.

11. Find the finance charge refund on a 24-month loan with monthly payments of $103.50 if you decide to pay off the loan with 10 months remaining. The finance charge is $215.55.

12. If you purchase a fishing boat for 18 monthly payments of $106 and an interest charge of $238, how much is the refund after 10 payments?

13. Find the interest on an average daily balance of $265 with an interest rate of .112%

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14. Find the finance charge on a credit card with an average daily balance of $465 if the rate charged is 1.25%.

15. Use the following activity chart for a credit card to find the unpaid balance on November 1. The billing cycle ended on October 31, and the finance charge is 1.5% of the average daily balance.

Date posted Activity Amount October 1 Billing date Previous balance $426.40 October 8 Purchase 41.60 October 11 Payment 70.00 October 16 Purchase 31.25 October 21 Purchase 26.80

Use Table 12-1 to find the annual percentage rate (APR) for the following exercises.

16. Find the annual percentage rate on a loan of $1,500 for 18 months if the loan requires $190 interest and is repaid monthly.

17. Find the annual percentage rate on a loan of $3,820 if the monthly payment is $130 for 36 months.

18. A vacuum cleaner was purchased on the installment plan with 12 monthly payments of $36.98 each. If the cash price was $415 and there was no down payment, find the annual percent- age rate.

19. A merchant charged $420 in cash for a dining room set that could be bought for $50 down and $40.75 per month for 10 months. What is the annual percentage rate?

20. An electric mixer was purchased on the installment plan for a down payment of $60 and 11 monthly payments of $11.05 each. The cash price was $170. Find the annual percentage rate.

21. A computer was purchased by paying $50 down and 24 monthly payments of $65 each. The cash price was $1,400. Find the annual percentage rate to the nearest tenth of a percent.

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EXERCISES SET B CHAPTER 12

NAME DATE

1. A television set has been purchased on the installment plan with a down payment of $120 and six monthly payments of $98.50. Find the installment price of the television set.

2. A dishwasher sold for a $983 installment price with a down payment of $150 and 12 monthly payments. How much is each payment?

3. What is the cash price of a chair if the installment price is $679, the finance charge is $102, and there was no down payment?

4. Find the refund fraction for a 42-month loan if it is paid in full with 16 months remaining.

Use the rule of 78 to find the finance charge refund in each of the following.

Finance Number of Remaining Interest charge monthly payments payments refund

5. $1,076 18 6

6. $476 12 5

7. $683 15 11

8. Find the refund fraction on a 48-month loan if it is paid off after 20 months.

9. Lanny Jacobs made a loan to purchase a computer. Find the refund due on this loan with interest charges of $657 if it is paid off after paying 7 of the 12 monthly payments.

10. Suppose you have borrowed money that is being repaid at $45 a month for 12 months. What is the finance charge refund after making eight payments if the finance charge is $105?

11. You have purchased a new stereo on the installment plan. The plan calls for 12 monthly payments of $45 and a $115 finance charge. After nine months you decide to pay off the loan. How much is the refund?

12. The interest for an automobile loan is $2,843. The automobile is financed for 36 monthly payments, and interest refunds are made using the rule of 78. How much interest should be refunded if the loan is paid in full with 22 months still remaining?

13. Find the finance charge on $371 if the interest charge is 1.4% of the average daily balance.

EXCEL

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14. A new desk for an office has a cash price of $1,500 and can be purchased on the installment plan with a 12.5% finance charge. The desk will be paid for in 12 monthly payments. Find the amount of the finance charge, the total price, and the amount of each monthly payment, if there was no down payment.

15. On January 1 the previous balance for Lynn’s charge account was $569.80. On the following days, purchases were posted:

January 13 $38.50 jewelry January 21 $44.56 clothing

On January 16 a $50 payment was posted. Using the average daily balance method, find the finance charge and unpaid balance on February 1 if the bank charges interest of 1.5% per month.

Use Table 12-1 to find the annual percentage rate for the following exercises.

16. Find the annual percentage rate on a loan for 25 months if the amount of the loan without interest is $300. The loan requires $40 interest.

17. Find the annual percentage rate on a loan of $700 without interest with 12 monthly payments. The loan requires $50 interest.

18. A queen-size brass bed costs $1,155 and is financed with monthly payments for three years. The total finance charge is $415.80. Find the annual percentage rate.

19. John Edmonds borrowed $500. He repaid the loan in 22 monthly payments of $26.30 each. Find the annual percentage rate.

20. A loan of $3,380 was paid back in 30 monthly payments with an interest charge of $620. Find the annual percentage rate.

21. A color enlarger costs $1,295 and is financed with monthly payments for two years. The total finance charge is $310.80. Find the annual percentage rate.

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PRACTICE TEST CHAPTER 12

1. Find the finance charge on an item with a cash price of $469 if the installment price is $503 and no down payment was made.

2. An item with a cash price of $578 can be purchased on the install- ment plan in 15 monthly payments of $46. Find the installment price if no down payment was made. Find the finance charge.

3. The installment price of a Bosch stainless steel refrigerator is $2,199.99 for an 18-month loan. If a $300 down payment has been made, find the installment payment.

4. The installment price of an Electrolux front-load washer is $1,299.90. What is the installment payment if a down payment of $295 is made and the loan is for 12 months?

5. A copier that originally cost $300 was sold on the installment plan at $28 per month for 12 months. Find the installment price if no down payment was made. Find the finance charge.

6. Use Table 12-1 to find the annual percentage rate for the loan in Exercise 3.

7. Use Table 12-1 to find the APR on a loan of $3,000 for three years if the loan had $810 interest and was repaid monthly.

8. Find the interest on an average daily balance of $165 if the monthly interest rate is 1 .34%

9. Find the yearly rate of interest on a loan if the monthly rate is 2%. 10. Find the interest refunded on a 15-month loan with total interest of $72 if the loan is paid in full with six months remaining.

11. Find the annual percentage rate on a loan of $1,600 for 24 months if $200 interest is charged and the loan is repaid in monthly payments. Use Table 12-1.

12. Find the annual interest rate on a loan that is repaid monthly for 26 months if the amount of the loan is $1,075. The interest charged is $134.85.

13. Office equipment was purchased on the installment plan with 12 monthly payments of $11.20 each. If the cash price was $120 and there was no down payment, find the annual percentage rate.

14. A canoe has been purchased on the installment plan with a down pay- ment of $75 and 10 monthly payments of $80 each. Find the install- ment price of the canoe.

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19. A 30-month loan that has interest of $3,987 is paid in full with 7 months remaining. Find the amount of interest to be refunded using the rule of 78.

20. Use the following activity chart to find the average daily balance, finance charge, and unpaid balance for July. The monthly interest rate is 1.75%. The billing cycle has 31 days.

Date Posted Activity Amount July 1 Billing date Previous balance $441.05 July 5 Payment $75.00 July 16 Purchase 23.50 July 26 Purchase 31.40

17. Maurice Van Norman made a 48-month loan that has interest of $1,987. He paid the loan in full with 11 months remaining. The inter- est is refunded based on the rule of 78. Find the amount of interest to be refunded.

18. Larry Williams made a 60-month loan that has interest of $2,518. He paid the loan in full with 21 months remaining. The interest is refunded based on the rule of 78. Find the amount of interest to be refunded.

15. Find the monthly payment when the installment price is $2,300, a down payment of $400 is made, and there are 12 monthly payments.

16. How much is to be financed on a cash price of $729 if a down payment of $75 is made?

21. Mary Lawson has a credit card account with an annual percentage rate of 18.24%. The unpaid balance for her November billing cycle is $783.56. During the billing cycle she purchased a desk chair for $134.77 and a floor mat for $82.36. Mary returned a grill purchased in the previous month for a credit of $186.21 and she made a payment of $80. If the account applies the unpaid balance method, what are the finance charge and the new balance?

22. Leslie Joiner has a credit card with an annual percentage rate of 17.4%. The unpaid balance for his June billing cycle is $2,156.28. During the billing cycle he purchased a refrigerator for $989.21 and a computer for $873.52. Leslie returned clothing purchased in May for a credit of $215.77 and made a payment of $425. If the account applies the unpaid balance method, what are the finance charge and the new balance?

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CRITICAL THINKING CHAPTER 12

1. Explain the mistake in the solution of the problem and correct the solution.

Dawn Mayhall financed a car and the loan of 42 months required $3,827 interest. She paid the loan off after making 20 payments. How much interest should be refunded if the rule of 78 is used?

Solution:

Thus, $890 should be refunded.

210

903 ($3,827) = $890

Refund fraction = 210

903

2. Explain the mistake in the solution and correct the solution. Ava Landry agreed to pay $2,847 interest for a 36-month loan to

redecorate her greeting card shop. However, business was better than expected and she repaid the loan with 16 months remaining. If the rule of 78 was used, how much interest should she get back?

Solution:

Thus, $1,265.33 should be refunded.

36 ($2,847) = $1,265.33

3. Arrange the consecutive numbers from 1 to 10 in ascending order, then in descending order, so that 1 and 10, 2 and 9, 3 and 8, and so on, align vertically. Add vertically. Find the grand total. Finally divide the grand total by 2. Compare the result to the sum of digits 1 through 10.

10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

4. Explain why finding the sum of consecutive numbers by using the process in Exercise 3 requires that the product be divided by 2.

5. Explain why the formula for finding the sum of consecutive numbers requires the product of the largest number and one more than the largest number rather than one less than the largest number.

6. Give three examples of finding the sum of consecutive odd numbers beginning with 1.

Challenge Problem It pays to read the details! Bank One Delaware offers a Platinum Visa Credit Card to qualifying persons with an introductory 0% fixed APR on all purchases and balance transfers and, after the 12-month introductory period, a low variable APR on purchases and balance transfers at a current annual rate of 8.99%. However, the default rate is 24.99% APR. A default occurs if the minimum payment is not received by the due date on the billing statement or if your bal- ance ever exceeds your credit limit. Find the difference in just one month’s interest on an average daily balance of $1,000 if the payment is not received by the due date.

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CASE STUDIES

12-1 Know What You Owe Nancy Tai has recently opened a revolving charge account with MasterCard. Her credit limit is $1,000, but she has not charged that much since opening the account. Nancy hasn’t had the time to review her monthly statements promptly as she should, but over the upcoming weekend she plans to catch up on her work. She has been putting it off because she can’t tell how much interest she paid or the unpaid balance in November. She spilled watercolor paint on that portion of the statement.

In reviewing November’s statement she notices that her beginning balance was $600 and that she made a $200 payment on November 10. She also charged purchases of $80 on November 5, $100 on November 15, and $50 on November 30. She paid $5.27 in interest the month before. She does remember, though, seeing the letters APR and the number 16%. Also, the back of her statement indicates that interest was charged using the average daily balance method, including current purchases, which considers the day of a charge or credit.

1. Find the unpaid balance on November 30 before the interest is charged.

2. Assuming a 30-day period in November find the average daily balance.

3. Calculate the interest for November.

4. What was the unpaid balance for November after interest is charged?

12-2 Massage Therapy It was time to expand her massage therapy business, and Arminte had finally found a commercial space that met her needs. With room for herself and the two new massage therapists she planned to hire, and adjacent to a chiropractor’s office, the space was everything that she had hoped for. Now all she needed was to finalize purchases for three massage rooms, furniture for the reception area, various artwork, and miscellaneous supplies. Arminte started to make a list of massage equipment: 3 tables at $1,695 each; 3 stools at $189 each; a portable massage chair for $399; and the list went on—bolsters, pillows, sheets, table warmers, and music. By the time Arminte was finished, her massage equipment alone totaled $7,644.25, including sales tax. The supplier offered in-house financing of 24 monthly payments at $325.33 per month, with a 10% down payment.

1. Find the amount financed, installment price, and the finance charge presuming Arminte goes with the financing available through her supplier.

2. Use Table 12-1 to find the annual percentage rate (APR) of the financing.

Source: Adapted from Winger and Frasca, Personal Finance: An Integrated Approach, 6th edition, Upper Saddle River, NJ: Prentice Hall, p. 162.

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453CONSUMER CREDIT

3. If Arminte takes the financing but pays the balance in full with 9 months remaining, what is the amount of the finance charge to be refunded using the rule of 78?

4. Arminte had recently opened a revolving charge account with MasterCard, to pick up some miscellaneous supplies for her business. Her credit limit is $1,500, with 18% APR. Her beginning balance for the month of April was $440, and she made a payment of $60, which was received on April 10. She purchased massage oil for $240 on April 6, office supplies for $68.45 on April 14, a CD player for $129.44 on April 20, and $25 in gas on April 27. Arminte’s statement indicates that interest is charged using the average daily balance method, including current purchases, which considers the day of a charge or credit. Assuming a 30-day period in April, find the average daily balance and the interest for April.

IS B

N 1

-2 56

-6 49

71 -6