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Simple Interest Section 5.1

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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.

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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.

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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.

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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

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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.

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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.

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Table summarizing the credit card history Time periodDay s Daily Balance June 10 – June 112$287.84 June 12 – June 176$287.84 + $45.60$333.44 June 18 – June 214$333.44 – $150.00$183.44 June 22 – July 211$183.44 + $20.00$203.44 July 3 – July 97$203.44 + $78.50$281.94

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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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