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# Simple Interest - PowerPoint PPT Presentation

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

Section 5.1

• 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.

• 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 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.

• 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

• 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.

• 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.

• 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