Simple Interest - Arizona State University

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Simple Interest
Section 5.1
Introduction
• When you deposit money into a savings at
a bank you expect the bank to pay you for
the privilege of saving your money with
them. This is extra money is called
interest.
• Interest is also paid by a borrower to a
lender for the privilege of using money.
• In this chapter we study the methods of
computing interest.
Simple Interest Formula
• The simple interest I on a principal (present
value) P at an annual interest rate r for t years is
I = Prt.
• The balance or future value F is given by
F = P + I = P + Prt = P(1 + rt).
• Example: calculate the simple interest on $1000
deposit at an annual interest rate of 5% for 2
years.
• ANSWER: I = ($1000)(.05)(2)=$100.
• Also the future value of the investment is
F = P + I = $1000 + $100 = $1100.
Add – on interest
• Add – on interest is a way of calculating
interest used by car dealerships, appliance
stores, furniture stores etc.
• The lender computes the simple interest
on the loan amount and adds that on to
the loan amount so that the interest is
distributed equally over each payment.
Add – on interest example
• A $1200 flat-screen TV is financed over a 2 year
period with 12% add-on interest. Find the
monthly payment.
• First calculate the simple interest on the loan:
$1200 x 0.12 x 2 = $288.
• The future value of the loan is
$1200 + $288 = $1488.
• Since the loan is for 2 years, there will be 24
monthly payments. Thus the monthly payment is
$1488/24=$62
Finance Charges
• Everyone who has a credit card knows
that if they do not pay-off their balance
each month they will be assessed a
monthly finance charge. How is this
computed???
• Credit card companies use the average
daily balance. The lender charges interest
for the actual number of days an amount
was owed on the bill.
Example of average daily balance
• Let’s look at George W. Bush’s credit card
statement. The APR is 21%.
• He’s carrying a balance of $287.84.
• On June 12 he got an oil change and for
his car. This cost $45.60.
• He made a payment of $150 on June 18.
• He then got gasoline for $20 on June 22.
• Then he got some PS-2 games for $78.50
on July 3.
Table summarizing the credit card
history
Time period
Day
Daily Balance
s
June 10 – June 11 2 $287.84
$287.84
June 12 – June 17
6
$287.84 + $45.60
$333.44
June 18 – June 21
4
$333.44 – $150.00 $183.44
June 22 – July 2
11
$183.44 + $20.00
$203.44
July 3 – July 9
7
$203.44 + $78.50
$281.94
Doing the calculations
• Avg. Daily Balance =
[2(287.84)+6(333.44)+4(183.44)+11(203.44)+7(281.94)]/
(2 + 6 + 4 + 11 + 7)
ADB = 7521.50/30 = $250.72
• Instead of using the annual percentage rate (APR), we
use the daily percentage rate for this account which is
.21/365. Also the time will be measured in days hence
t = 30. Use the simple interest formula to compute the
finance charge.
• Finance charge = 250.72 x (.21/365) x 30 = $4.33
• The new balance on W’s credit card will be $281.94 +
$4.33 = $286.27

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