Math- Quantitative Literacy

Torie

Chapter4.pptx

Home >Business & Finance homework help >Management homework help >Math- Quantitative Literacy

Quantitative Literacy: Thinking Between the Lines

Third Edition

Chapter 4

Personal Finance

Lesson Plan

Saving money: The power of compounding

Borrowing: How much car can you afford?

Savings for the long term: Build that nest egg

Credit cards: Paying off consumer debt

Inflation, taxes, and stocks: Managing your money

4.1 Saving money: The power of compounding (1 of 19)

Principal: The initial balance of an account.

Simple interest: calculated by applying the interest rate to the principal only, not to interest earned.

Simple Interest Formula

Simple interest earned =

Principal × Yearly interest rate (as a decimal) × Time in years

4.1 Saving money: The power of compounding (2 of 19)

Example: We invest $2000 in an account that pays simple interest of 4% each year. Find the interest earned after five years.

Solution: The interest rate of 4% written as a decimal is 0.04.

Simple interest earned

= Principal × Yearly interest rate × Time in years

= $2000 × 0.04/year × 5 years

= $400

4.1 Saving money: The power of compounding (3 of 19)

Compound interest is paid on the principal and on the interest that the account has already earned. In short, compound interest includes interest on the interest.

Example: Suppose that $1000 is invested in an account earning 10% interest compounded annually.

After one year the account earns 10% of $1000 or $100—the same as with simple interest.

At the end of the second year, the account earns 10% of $1100 or $110. The account balance is $1210 when the interest is compounded annually, but the account balance is only $1200 for simple interest.

4.1 Saving money: The power of compounding (4 of 19)

Simple and Compound Interest Comparison

End of year	Simple interest: Interest	Simple interest: Balance	Simple interest: Growth
1	10% of $1000 = $100	$1100	$100
2	10% of $1000 = $100	$1200	$100
3	10% of $1000 = $100	$1300	$100
10	$100	$2000
50	$100	$6000

Yearly compounding: Interest	Yearly compounding: Balance	Yearly compounding: Growth
10% of $1000 = $100	$1100	$100
10% of $1100 = $110	$1210	$110
10% of $1210 = $121	$1331	$121
$235.79	$2593.74
$10,671.90	$117,390.85

4.1 Saving money: The power of compounding (5 of 19)

Period interest rate – the interest rate for a given compounding period, for example one month. This formula uses the annual percentage rate, APR.

Period interest rate

Example: The period interest rate for $500 invested at 6% compounded monthly would be

4.1 Saving money: The power of compounding (6 of 19)

Compound interest – interest paid on both the principal and the interest the account has earned.

FORMULA 4.3 Compound Interest Formula

Balance after t periods

Alternatively, we can write the formula as

Where interest is compounded n times per year and y is the number of years. This form is equivalent since and the number of periods is .

4.1 Saving money: The power of compounding (7 of 19)

Example: Suppose we invest $10,000 in a five-year certificate of deposit (CD) that pays an APR of 6%. What is the value of the mature CD if interest is:

compounded annually?

compounded quarterly?

compounded monthly?

compounded daily?

4.1 Saving money: The power of compounding (8 of 19)

Solution:

Compounded annually: the rate is the same as the APR:

r = 6% = 0.06 and t = 5 years.

Balance after 5 years

4.1 Saving money: The power of compounding (9 of 19)

Solution:

Compounded quarterly:

5 years is 5 × 4 quarters, so t = 20 in compound interest formula:

Balance after 5 years

4.1 Saving money: The power of compounding (10 of 19)

Solution:

Compounded monthly:

5 years is 5 × 12 months, so t = 60;

Balance after 5 years

4.1 Saving money: The power of compounding (11 of 19)

Solution:

Compounded daily:

5 years is 5 × 365 = 1825 days.

Balance after 5 years

4.1 Saving money: The power of compounding (12 of 19)

Solution:

We summarize the results.

Compounding period	Balance at maturity
Yearly	$13,382.26
Quarterly	$13,468.55
Monthly	$13,488.50
Daily	$13,498.26

4.1 Saving money: The power of compounding (13 of 19)

The Annual Percentage Yield (APY) – the actual percentage return earned in a year.

APY =

Where n is the number of compounding periods per year.

4.1 Saving money: The power of compounding (14 of 19)

Example: You have an account that pays APR of 10%. If interest is compounded monthly, find the APY.

Solution: APR = 10% = 0.10, n = 12 , so we use the APY formula:

APY =

Round the answer as a percentage to two decimal places; the APY is about 10.47%.

4.1 Saving money: The power of compounding (15 of 19)

APY Balance Formula

Balance after y years = Principal × (1+APY)y

Example: In March 2014, a bank offered a five-year CD at 1.09% APY. If you buy a $100,000 CD, calculate the balance at maturity.

Solution: APY = 1.09% = 0.0109, y = 5, and so we use APY balance formula:

4.1 Saving money: The power of compounding (16 of 19)

Present value: the amount we initially invest.

Present value = Principal

Future value: the value of that investment at some specific time in the future.

Future value = balance after t periods

Compound Interest Formula

4.1 Saving money: The power of compounding (17 of 19)

Example: You would like to have $10,000 to buy a car three years from now. How much would you have to invest now in a savings account that pays an APR of 9% compounded monthly.

Solution: = 36:

Therefore, we should invest $7641.49 now.

4.1 Saving money: The power of compounding (18 of 19)

Exact doubling time for investments

where r is the period interest rate as a decimal.

Approximate doubling time using the rule of 72

where APR is expressed as a percentage.

4.1 Saving money: The power of compounding (19 of 19)

Example: Suppose an account has an APR of 8% compounded quarterly. Estimate the doubling time using the rule of 72. Calculate the exact doubling time.

Solution: The rule of 72 gives the estimate doubling time 9 years.

To find the exact doubling time, since the period is a quarter.

Thus, the actual doubling time is 35.0 quarters, or 8 years and 9 months.

4.2 Borrowing: How much car can you afford? (1 of 20)

With an installment loan you borrow money for a fixed period of time, called the term of the loan, and you make regular payments (usually monthly) to pay off the loan plus interest accumulated during that time.

The amount of each payment depends on three things:

the amount of money we borrow (the principal)

the interest rate (or APR)

the term of the loan

4.2 Borrowing: How much car can you afford? (2 of 20)

Monthly payment formula

where t is the term in months and r=APR/12 is the monthly rate as a decimal.

Example (College Loan): You need to borrow $5000 so you can attend college next fall. You get the loan at an APR of 6% to be paid off in monthly installments over three years.

Calculate monthly payment.

What is the total of all payments?

How much interest was paid in all?

4.2 Borrowing: How much car can you afford? (3 of 20)

Solution: 1. The interest rate (or APR): APR of 6%

The monthly rate as a decimal is:

We want to pay off the loan in three years, so we use a term of

in the monthly payment formula:

4.2 Borrowing: How much car can you afford? (4 of 20)

Solution:

What is the total of all payments?

There are 36 payments of $152.11 each, so the total of all payments is

36 × $152.11 = $5475.96

How much interest was paid in all?

Because the total payments are $5475.96, of which $5000 was the amount borrowed, the difference,

$5475.96 – 5000 = $475.96

is the amount of interest paid over the life of the loan.

4.2 Borrowing: How much car can you afford? (5 of 20)

Suppose you can afford a certain monthly payment, how much can you borrow to stay within that budget?

FORMULA 4.7 Companion Monthly Payment Formula

Alternatively, we can write the formula as

Where y is the number of years.

4.2 Borrowing: How much car can you afford? (6 of 20)

Example (Buying a car): We can afford to make payments of $250 per month for three years. Our car dealer is offering us a loan at an APR of 5%. For what price automobile should we be shopping?

Solution:

We should shop for cars that cost $8341.43 or less.

4.2 Borrowing: How much car can you afford? (7 of 20)

Example: Suppose we need to borrow $15,000 at an APR of 9% to buy a new car.

What will the monthly payment be if we borrow the money for

We find we cannot afford the $15,000 car because we can only afford a monthly payment of $300. What price car can we shop for if the dealer offers a loan at 9% APR for a term of

4.2 Borrowing: How much car can you afford? (8 of 20)

Solution: 1. The monthly rate as a decimal is

We are paying off the loan in years, so months. Therefore, by the monthly payment formula (Formula 4.6),

4.2 Borrowing: How much car can you afford? (9 of 20)

Solution:

The monthly rate as a decimal is r = 0.0075, and there are still 42 payments. We know that the monthly payment we can afford is $300. We use the companion formula (Formula 4.7) to find the amount we can borrow on this budget:

This means that we can afford to shop for a car that costs no more than $10,774.11.

4.2 Borrowing: How much car can you afford? (10 of 20)

Amortization table (schedule): shows for each payment made the amount applied to interest, the amount applied to the balance owed, and the outstanding balance.

If you borrow money to pay for an item, your equity in that item at a given time is the part of the principal you have paid.

Example: Suppose you borrow $1000 at 12% APR to buy a computer. We pay off the loan in 12 monthly payments. Make an amortization table showing payments over the first five months. What is your equity in the computer after five payments?

4.2 Borrowing: How much car can you afford? (11 of 20)

Solution:

The monthly rate as a decimal.

The monthly payment formula with

4.2 Borrowing: How much car can you afford? (12 of 20)

Make our 1st payment: the outstanding balance is $1000

Interest = 1% of $1000 = $10

$88.85 – $10 = $78.85 to interest, and the outstanding balance

Balance owed after 1 payment

=$1000−$78.85=$921.15

4.2 Borrowing: How much car can you afford? (13 of 20)

Make our 2nd payment: the outstanding balance is $921.15

Interest = 1% of $921.15 = $9.21

$88.85 – $9.21 = $79.64 to interest, and the outstanding balance.

Balance owed after 2 payments

=$921.15 − $79.64 = $841.51

4.2 Borrowing: How much car can you afford? (14 of 20)

If we continue in this way, we get the following table:

Payment number	Payment	Applied to interest	Applied to balance owed	Outstanding balance
				$1000.00
1	$88.85	1% of $1000.00 = $10.00	$78.85	$921.15
2	$88.85	1% of $921.15 = $9.21	$79.64	$841.51
3	$88.85	1% of $841.51 = $8.42	$80.43	$761.08
4	$88.85	1% of $761.08 = $7.61	$81.24	$679.84
5	$88.85	1% of $676.84 = $6.80	$82.05	$597.79
6	$88.85	1% of $597.79 = $5.98	$82.87	$514.92

Equity after six payments = $1000 − $514.92 = $405.08.

4.2 Borrowing: How much car can you afford? (15 of 20)

Example: You borrow $150,000 at an APR of 6% to purchase a plot of land. You pay off the loan in monthly payments over 10 years.

Find the monthly payment.

Complete the four-month amortization table.

What is your equity in the land after four payments?

4.2 Borrowing: How much car can you afford? (16 of 20)

Solution:

The monthly rate is . As a decimal, this is . We use the monthly payment formula with months:

4.2 Borrowing: How much car can you afford? (17 of 20)

Solution: 2.

Payment number	Payment	Applied to interest	Applied to balance owed	Outstanding balance
				$150,000.00
1	$1665.31	0.5% of $150,000.00 = $750.00	$915.31	$149,084.69
2	$1665.31	0.5% of $149,084.69 = $745.42	$919.89	$148,164.80
3	$1665.31	0.5% of $148,164.80 = $740.82	$924.49	$147,240.31
4	$1665.31	0.5% of $147,240.31 = $736.20	$929.11	$146,311.20

The table from Part 1 tells us that after four payments we still owe $146,311.20. So our equity is

Equity after 4 months = $150,000 - $146,311.20 = $3688.80

4.2 Borrowing: How much car can you afford? (18 of 20)

Home Mortgage: a loan for the purchase of a home.

Example (30-year mortgage): You decide to take a 30-year mortgage for $300,000 at an APR of 9%. Find the total interest paid.

Solution:

The loan is for 30 years: 𝑡=30×12=360 months in the monthly payment formula:

Total amount paid = 360 × $2413.87 = $868,993.20

Total interest paid = $868,993.20 - $300,000 = $568,993.20

4.2 Borrowing: How much car can you afford? (19 of 20)

Fixed-rate mortgage: keeps the same interest rate over the life of the loan.

Adjustable-rate mortgage (ARM): the interest may vary over the life of the loan.

Example (Comparing monthly payment): Fixed-rate mortgage and ARM.

We want to borrow $200,000 for a 30-year home mortgage. We have found an APR of 6.6% for a fixed-rate mortgage and an APR of 6% for an ARM. Compare the initial monthly payments for these loans.

4.2 Borrowing: How much car can you afford? (20 of 20)

Solution: principal = $200,000 and t = 360 months.

Fixed-rate: The monthly payment formula gives:

ARM: The monthly payment formula gives:

4.3 Saving for the long term: Build that nest egg (1 of 14)

Example: You deposit $100 to your savings account at the end of each month and suppose the account pays a monthly rate of 1% on the balance in the account. Find the balance at the end of three months.

Solution:

At the end of 1st month: New balance = Deposit = $100

At the end of 2nd month: New balance = Previous balance + Interest + Deposit = $100 + (1%×$100=$1) + $100 = $201

At the end of 3rd month: New balance = Previous balance + Interest + Deposit = $201 + (1%×$201=$2.01) + $100 = $303.01

4.3 Saving for the long term: Build that nest egg (2 of 14)

TABLE 4.2 Regular Deposits into an Account

At end of month number	Interest paid on previous balance	Deposit	Balance
1	$0.00	$100	$100.00
2	1% of $100.00 = $1.00	$100	$201.00
3	1% of $201.00 = $2.01	$100	$303.01
4	1% of $303.01 = $3.03	$100	$406.04
5	1% of $406.04 = $4.06	$100	$510.10
6	1% of $510.10 = $5.10	$100	$615.20
7	1% of $615.20 = $6.15	$100	$721.35
8	1% of $721.35 = $7.21	$100	$828.56
9	1% of $828.56 = $8.29	$100	$936.85
10	1% of $936.85 = $9.37	$100	$1046.22

4.3 Saving for the long term: Build that nest egg (3 of 14)

Regular deposits balance: regular deposits at the end of each period.

Regular deposit formula

Example: Suppose we have a savings account earning 7% APR. We deposit $20 to the account at the end of each month for five years. What is the account balance after five years?

4.3 Saving for the long term: Build that nest egg (4 of 14)

Solution: The monthly interest rate The number of deposits . The regular deposit formula gives:

The future value is $1431.86.

4.3 Saving for the long term: Build that nest egg (5 of 14)

Determining the savings needed

Deposit needed formula

Example (Saving for college): How much does your younger brother need to deposit each month into a savings account that pays 7.2% APR in order to have $10,000 when he starts college in five years?

4.3 Saving for the long term: Build that nest egg (6 of 14)

Solution: We want to achieve a goal of $10,000 in five years.

The monthly interest rate

The number of deposits t = 5 × 12=60. The deposit needed formula gives:

He needs to deposit $138.96 each month.

4.3 Saving for the long term: Build that nest egg (7 of 14)

Example (Saving for retirement): Suppose that you’d like to retire in 40 years and you want to have a future value of $500,000 in a savings account, and suppose that your employer makes regular monthly deposits into your retirement account. If you expect an APR of 9% for your account, how much do you need your employer to deposit each month?

4.3 Saving for the long term: Build that nest egg (8 of 14)

Solution: Goal = $500,000, t = 40 12 = 480

r = Monthly rate =

4.3 Saving for the long term: Build that nest egg (9 of 14)

Example: Assume the interest rate is constant over the period in question. Over a period of 40 years interest rates can vary widely. Assume a constant APR of 6% for your retirement account. How much do you need your employer to deposit each month under this assumption?

4.3 Saving for the long term: Build that nest egg (10 of 14)

Solution: r = Monthly rate =

Note that the decrease in the interest rate from 9% to 6% requires that the monthly deposit more than doubles.

4.3 Saving for the long term: Build that nest egg (11 of 14)

Nest egg: the balance of your retirement account at the time of retirement.

Monthly yield: the amount you can withdraw from your retirement account each month.

An Annuity: an arrangement that withdraws both principal and interest from your nest egg.

Annuity Yield Formula

4.3 Saving for the long term: Build that nest egg (12 of 14)

Example: Suppose we have a nest egg of $800,000 with an APR of 6% compounded monthly. Find the monthly yield for a 20-year annuity.

Solution: months.

= $5731.45

4.3 Saving for the long term: Build that nest egg (13 of 14)

Annuity Yield Goal

Example: Suppose our retirement account pays 5% APR compounded monthly. What size nest egg do we need in order to retire with 20-year annuity that yields $4000 per month?

4.3 Saving for the long term: Build that nest egg (14 of 14)

Solution:

4.4 Credit cards: Paying off consumer debt (1 of 19)

Credit card basics:

Amount subject to finance charges

= Previous balance – Payment + Purchases

Where the finance charge is calculated by applying monthly interest rate (r = APR/12) to this amount.

New balance = Amount subject to finance charges + Finance charge

4.4 Credit cards: Paying off consumer debt (2 of 19)

Example: Suppose your Visa card calculates finance charges using an APR of 22.8%. Your previous statement showed a balance of $500, in response to which you made a payment of $200. You then bought $400 worth of clothes, which you charged to your Visa card. Find a new balance after one month.

4.4 Credit cards: Paying off consumer debt (3 of 19)

Solution:

Amount subject to finance charges

= Previous balance – Payment + Purchases

= $500 – $200 + $400 = $700

Finance charge = $13.30

New Balance

= Amount subject to finance charges + Finance charge

= $700 + $13.30 = $713.30

	Previous balance	Payments	Purchases	Finance charge	New balance
Month 1	$500	$200	$400	1.9% of $700 = $13.30	$713.30

4.4 Credit cards: Paying off consumer debt (4 of 19)

Example: We have a card with an APR of 24%.

The minimum payment is 5% of the balance. Suppose we have a balance of $400 on the card.

We decide to stop charging and to pay it off by making the minimum payment each month.

Calculate the new balance after we have made our first minimum payment, and then calculate the minimum payment due for the next month.

4.4 Credit cards: Paying off consumer debt (5 of 19)

Solution:

1st minimum payment = 5% of balance = 0.05 × $400 = $20

Amount subject to finance charges

= Previous balance – Payment + Purchases

= $400 – $20 + $0 = $380

Finance charge

4.4 Credit cards: Paying off consumer debt (6 of 19)

New Balance

= Amount subject to finance charges + Finance charge

= $380 + $7.60 = $387.60

The next minimum payment will be 5% of $387.60.

Minimum payment = 5% of balance = 0.05 × $387.60 = $19.38

4.4 Credit cards: Paying off consumer debt (7 of 19)

Minimum payment balance

Minimum payment balance formula

4.4 Credit cards: Paying off consumer debt (8 of 19)

Where r is the monthly rate and m is the minimum monthly payment as a percent of the balance.

Example: We have a card with an APR of 20% and a minimum payment that is 4% of the balance. We have a balance of $250 on the card, and we stop charging and pay off that balance by making the minimum payment each month.

Find the balance after two years of payments.

4.4 Credit cards: Paying off consumer debt (9 of 19)

Solution:

The monthly interest rate:

The minimum payment = 4% of new balance: m = 0.04

The initial balance = $250

The number of payments: t = 2 × 12 = 24 months

4.4 Credit cards: Paying off consumer debt (10 of 19)

4.4 Credit cards: Paying off consumer debt (11 of 19)

Example: Suppose you have a balance $10,000 on your Visa card, which has an APR of 24%. The card requires a minimum payment of 5% of the balance. You stop charging and begin making only the minimum payment until your balance is below $100.

Find a formula that gives your balance after t monthly payments.

Find your balance after five years of payments.

4.4 Credit cards: Paying off consumer debt (12 of 19)

Determine how long it will take to get your balance under $100.

Suppose that instead of the minimum payment, you want to make a fixed monthly payment so that your debt is clear in two years. How much do you pay each month?

4.4 Credit cards: Paying off consumer debt (13 of 19)

Solution:

The minimum payment as a decimal: m = 0.05.

The monthly rate: r = 0.24/12 = 0.02

The initial balance = $10,000

4.4 Credit cards: Paying off consumer debt (14 of 19)

Now five years: t = 5 × 12 = 60 months

Balance after 60 months = $10,000 × 0.96960 = $1511.56

After five years, we still owe over $1500.

4.4 Credit cards: Paying off consumer debt (15 of 19)

Determine how long it takes to get the balance down to $100.

Method 1 (Using a logarithm): Solve for t the equation

$100 = $10,000 × 0.969𝑡

Divide each side of the equation by $10,000:

4.4 Credit cards: Paying off consumer debt (16 of 19)

Solve exponential equation using logarithm:

Use this formula: months.

Hence, the balance will be under $100 after 147 monthly payments.

4.4 Credit cards: Paying off consumer debt (17 of 19)

Determine how long it takes to get the balance down to $100.

Method 2 (Trial and error): If you want to avoid logarithms, you can solve this problem using trial and error with a calculator. The information in part 2 indicates that it will take some time for the balance to drop below $100.

Try five years or 120 months,

Balance after 120 months = $10,000 × 0.969120 = 228.48.

4.4 Credit cards: Paying off consumer debt (18 of 19)

So we should try a large number of months. If you continue in this way, we find the same answer as that obtained for Method 1: the balance drops below $100 at payment 147.

4.4 Credit cards: Paying off consumer debt (19 of 19)

Consider your debt as an installment loan:

Amount borrowed = $10,000

Monthly interest rate r = APR/12 = 24%/12 = 0.02

Pay off the loan over 24 years: t = 24

Use the monthly payment formula from section 4.2:

So, a payment of $528.71 each month will clear the debt in two years.

4.5 Inflation, taxes, and stocks: Managing your money (1 of 10)

Consumer Price Index (CPI): a measure of the average price paid by urban consumers for a “market basket” of consumer goods and services.

Inflation: an increase in prices.

The rate of inflation: measured by the percentage change in the CPI over time.

Deflation: when prices decrease, the percentage change is negative.

4.5 Inflation, taxes, and stocks: Managing your money (2 of 10)

Example: Suppose the CPI increases this year from 200 to 205. What is the rate of inflation for this year?

Solution:

The change in CPI = 205 – 200 = 5.

The percentage change

Thus, the rate of inflation is 2.5%.

4.5 Inflation, taxes, and stocks: Managing your money (3 of 10)

Buying Power Formula

Where i is the inflation rate expressed as a percent (not a decimal).

Example: Suppose the rate of inflation this year is 5%. What is the percentage decrease in the buying power of a dollar?

Solution: 𝑖 = 5%

This is about 4.8%.

4.5 Inflation, taxes, and stocks: Managing your money (4 of 10)

Inflation Formula

Where B is the decrease in buying power expressed as a percent (not a decimal).

Example: Suppose the buying power of a dollar decreased by 2.5% this year. What is the rate of inflation this year?

Solution: B = 2.5%

This is about 2.6%.

4.5 Inflation, taxes, and stocks: Managing your money (5 of 10)

Example (Calculating the tax: a single person): In the year 2016, Alex was single and had a taxable income of $70,000. How much tax did she owe?

Solution: Schedule X – Use if your filing status is Single

If Taxable Income: Is over	If Taxable Income: But not over	The Tax is: This amount	The Tax is: Plus this %	The Tax is: Of the excess over
$0	$9275		10%	$0
9276	37,650	$927.50	15%	9275
37,651	91,150	5183.75	25%	37,650
91,151	190,150	18,558.75	28%	91,150
190,151	413,350	46,278.75	33%	190,150
413,351	415,050	119,934.75	35%	413,350
415,051		120,529.75	39.6%	415.050

4.5 Inflation, taxes, and stocks: Managing your money (6 of 10)

According to Table 4.5, Alex owed $5183.75 plus 25% of the excess taxable income over $37,650. The total tax is

$5183.75+0.25×($70,000-$37,650)=$13,271.25

4.5 Inflation, taxes, and stocks: Managing your money (7 of 10)

Example: In the year 2016, Betty and Carol were single, and each had a total income of $75,000. Betty took a deduction of $10,000 but had no tax credits.

Carol took a deduction of $9000 and had an education tax credit of $1000. Compare the taxes owed by Betty and Carol.

4.5 Inflation, taxes, and stocks: Managing your money (8 of 10)

Solution:

Betty: the taxable income = $75,000 – $10,000 = $65,000.

By Table 4.5, Betty owes $5183.75 plus 25% of the excess taxable income over $37,650. The total tax is:

$5183.75 + 0.25 × ($65,000 − $37,650) = $12,021.25

Betty has no tax credits, so the tax she owes is $12,021.25.

4.5 Inflation, taxes, and stocks: Managing your money (9 of 10)

Carol: the taxable income = $75,000 – $9000 = $66,000.

By Table 4.5, Carol owes $5183.75 plus 25% of the excess taxable income over $37,650. The total tax is:

$5183.75 + 0.25 × ($66,000 - $37,650) = $12,271.25

Carol has a tax credit of $1000, so the tax she owes is:

$12,271.25 − $1000 = $11,271.25

Betty owes:

$12,021.25 − $11,271.25 = $750.00

more tax than Carol.

4.5 Inflation, taxes, and stocks: Managing your money (10 of 10)

For every $1 move in any Dow company’s stock price, the Dow Jones Industrial Average (DJIA) changes by about 6.85 points.

Example (Finding changes in the Dow): Suppose the stock of Walt Disney increases in value by $3 per share. If all other Dow stock prices remain unchanged, how does this affect the DJIA?

Solution: Each $1 increases causes the average to increase by about 6.85 points. So, $3 increase would cause an increase of about 3 × 6.85 = 20.55 points in the Dow.

Chapter Summary (1 of 2)

Savings: simple interest or compound interest

Formulas: simple interest earned

period interest rate

balance after t periods

APY

Present value or Future value

Number of periods to double

Borrowing: an installment loan

Formulas: Monthly payment

Amount borrowed

Fixed-rate mortgage vs. ARM

Chapter Summary (2 of 2)

Saving for the long term: Build the nest egg (Annuity)

Formulas: Balance after t deposits

Needed deposit

Monthly annuity yield

Nest egg needed

Credit cards

Formulas: Amount subject to finance charges

Balance after t minimum payments

Inflation, taxes, and stocks

Understand CPI, taxes, DJIA