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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.

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simple interest

Simple Interest

Section 5.1

introduction
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
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
  • 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
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
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
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.
doing the calculations
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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