easy paper
snoopy beats
h__4._ch._5.pdf
1
FINANCE Ch. # 5
5.1 Simple Interest
Objectives
Make simple interest calculations
Determine a credit card finance charge
Find the payment required by an add-on-interest loan
Interest is money paid for the use of money.
The principal is the amount of the deposit or loan.
The interest rate is a percent of the principal.
The time is the length of time for which the money is borrowed or lent.
Simple Interest Formula (Add – on)
Interest = Principal x rate x Time.
I = amount of interest.
p = principal.
r = annual interest rate.
t = time (in years).
Ex:
How much interest will you earn in three years with an initial deposit of $300.00, where
the rate is 5% annually?
Future Value
The future value is the amount that you will have after the interest is added to the
principal.
Interest for part of the year
Exact interest: 365 days per year
Ordinary interest: 360 days per year.
Most businesses use ordinary interest. So use 360 for the number of days in a year.
Add-on-Interest Loan
To find the monthly payment of an add-on interest loan:
1. Find P, the loan amount. 2. Use the simple interest formula to find I. 3. Find the amount to be repaid by adding on the interest I to the loan amount P. 4. Divide the result by the number of payments.
I P r t
FV P I
2
Credit Card Finance Charge
To find the credit card finance charge with the average daily balance method:
1. Find the balance for each day in the billing period and the number of days at that balance.
2. The average daily balance is the weight average of these daily balances, weighted to Reflect the number of days at that balance.
3. The finance charge is simple interest applied to average daily balance.
The number of days from August 2 to August 30 is: 30 – 2 = 28 days
The number of days from August 2 through August 30 is: 30 – 2 + 1 = 29 days
This count includes August 2 and August 30.
Ex:
The activity on Tom’s Visa accounts for one billing period (October 15 through November
14), the previous balance was $346.57, and the annual interest rate is 21%, Given:
a. Find the average daily balance.
b. Find the finance charge.
a.
Time Interval Days Daily Balance
Oct. 15 through Oct. 20 20 – 14 = 6 $346.57
Oct. 21 through Oct. 22 22 – 20 = 2 $346.57 – $50 = $296.57
Oct. 23 through Nov. 6 31 – 22 = 9, 9 + 6 = 15 $296.57 + $42.14 = $338.71
Nov.7 through Nov. 14 14 – 6 = 8 $338.71 + $18.55 = $357.26
Average daily balance (6)($346.57) (2)($296.57) (15)$338.71 (8)(357.26)
6 2 15 8
$342.29967 $342.30
b. I P r t
31 (342.829967)(0.21) $6.11
365 I
Oct. 21 Payment $50
Oct. 23 Restaurant $42
Nov. 7 Clothing $18.55
3
Ex:
Find the amount of money that must be invested now at a simple interest so that it will be
worth $1,000 in two years given r = 0.05759
Solution:
We are asked to find the principal P that will generate a future value of $1,000.
We are given 1FV P rt
1 (0.05759)(2)FV P
1000
896.86099 $896.86 [1 (0.0575)(2)]
P
Ex:
1. Suppose that you barrow $1000.00 on Jan. 1 at 10% simple interest. How much interest accrues (accumulate) to May 28 (180 days later)? What is the total amount that must be
repaid?
2. Find the future value of $5,000 deposited in an account earning 7.5% simple interest in 5 years.
3. You need $5,000 per month on which to live in retirement. If the interest rate is 10.5%, how much must have in the bank when you retire so you can live on interest only?
4. Suppose you want to save $3650, and you put $3000 in the bank at 8% simple interest. How long it take?
4
5.2 Compound Interest
Objectives
Understand the difference between simple interest and compound interest
Use Compound Interest Formula
Understand and Compute the annual yield.
Compounding Interest
Most banks do not pay interest according to the simple interest
formula; after some period of time, they add the interest to the
principal and then pay interest on this new, larger amount.
When this is done, it is called compound interest.
Most banks compound interest more than once a year.
Semiannually: twice a year. Quarterly: 4 times a year. Monthly: 12 times a year.
Daily: 360 times a year.
We can summarize the variables we use for interest.
A = future value Principal plus interest.
P = principal.
r = interest rate this is the annual interest rate.
t = time this the time in years.
n = number of compounding periods each year. (n = 1 for annual, n = 2 for semiannual)
Ex:
1. Find the future value of $5,000 invested for 7 years at 10% interest. a. Compounded annually. b. Compounded semiannually. c. Compounded quarterly. d. Compounded Daily.
2. Suppose you are over 21 years old and will make monthly deposits to a bank account paying 10% compounded monthly. Which is the better option?
a. Deposit $200 per month for 5 – years and leave the balance until age 65. b. Wait until you are 40 – years old, then deposit $ 200 per month until you age 65. c. How much did you invested in each option?
3. Find the time needed to double the amount $ 8,000 if the rate 4,5% compounded monthly.
.
1
n t r
A P n
5
5.4 Amortized Loans
Objectives
Understand what an amortized loan
Learn how to do home loan and car loan computations
Learn how to make and use an amortization schedule.
An Amortized loan is a loan for which the loan amount, plus interest, is paid off with a series of
regular equal payments.
A simple interest loan is a loan whose interest is simple computed on the principle that is owed.
The current balance is the principle that is currently owed.
A simple interest amortized loan is a loan that is a simple interest loan and also an amortized
loan.
Amortization is the process of paying off a debt by systematically making partial payments until
the debt and accrued interest are repaid.
Present Value of an Annuity Formula
If the periodic payment is known ( pymt ) and you wish to find the present value of those
periodic payments, use the present value of an annuity formula:
Amortization Schedules Steps
For each payment, list the payment number, principle portion, interest portion, total
payment, and balance.
For each payment:
1. Find the interest on the balance, using Interest portion . .I P r t , where P is the unpaid
principle or balance.
For each payment except the last:
2. Principle portion total payment interest portion
3. Balance previous balace - principle portion
For last payment:
4. Principle portion previous balance
5. Total payment principle portion + interest portion
.
1 1
n t r
n P pymt
r
n
6
Unpaid Balance Formula
Unpaid balance current value of loan amount current valueof annuity
1 1
(1 )
n
n i
P i pymt i
Where pymt is the loan payment, i is the periodic interest rate, n is the number of
periods from the beginning of the loan to the present, and P is the loan amount.
Ex:
A house for $140,000. They paid the sellers a 20% down payment and obtained a simple
interest amortized loan for $112,000 from their bank at 3 4
10 % for 30- years. Their monthly
payment is $1,045.50, payments was made for 10-years.
Find the cost of paying off the existing loan.
Solution
Unpaid balance
= current value of loan amount – current value of annuity
120
120
1 1 (1 )
0.1075 1 1
0.1075 12 112, 000 1 1, 045.50 $102, 981.42
0.107512
12
n
n i
P i pymt i
After ten years of payments of $1045.50 a month on a loan of $112,000, still owe
$102,981.42
At the beginning of the loan, you owe a lot of money, so most of each payment is
interest, and very little is principal.
Later, you do not owe as much, so most of each payment is principal and very little is
interest.
EX
1. How much you save in 8-years if you deposit $150 at the end of each month into an account paying 10.5 % compounded monthly?
2. You want to purchase a home for $225,000 with a 30-years mortgage at 7.5 % Interest. You can put 30 % down. Find the monthly payment?
3. Suppose your goal is $25,000 in 5-years, you can obtain 8.5 % compound monthly. Find: a. The amount of deposit you need now.
b. What is the amount of monthly payment if you want to deposit in a sinking fund?
7
4. You can afford $250 / month for a car. What is the max- loan if the interest is 12% and you want to pay the loan in 5-years?
5. Compare the future value if you: Deposit $100 / month for 5-years; leave it for 40-years.
Deposit $100 / month for 25-years, with interest rate 12% compounded monthly
6. You want $10,000 in 5-years; you obtain interest rate 6.75 % compounded monthly. How much you deposit now?
7. An insurance policy pays $10,000 in 5-years. What lump-sum deposit today will yield $10,000 in 5-years? Assuming a 10 % interest rate compounded annually.
8. Find the amount of interest, the monthly payment and the APR for a $5,000 loan at 12% add-on rate for 5 years.
9. A lottery prize pays $ 50, 000 per year for the next 20 years. If the current rate of return is 12.25 %, what is the present value of this prize?
10. Suppose that you expect to receive a $ 100,000 inheritance in 3 years and 4-months. What is the present value of your inheritance if the current rate is 6.4% compounded
monthly?
11. An insurance policy offers you the option of being paid $750 per month. For 20 years, or a lump sum of $ 50,000. Which has more value if the current rate of return is 9.5%
compounded monthly, and you expect to live for 20-years?
12. A lottery offers a $1,000,000 prize to be paid in 29 equal installments of $ 20,000 with a 30
th . Final payment of $ 420,000. What is the total value of this annuity if the current
annual rate is 5 %? ($ 1,666,454.24)
