10.2 Personal Loans and Simple Interest 597 Example 3 A Pawn Loan To obtain money to pay some medical bills, Kevin decides to pawn his bicycle. Kevin borrows $300 and after 30 days gets his bicycle back by paying the pawn broker $355. What annual rate of interest did Kevin pay? Solution Kevin paid $355 $300 $55 − = in interest, and the length of the loan is for 30 days or 30 360 1 12 = of a year. Using the formula i prt, = we get r r r r $55 $300 1 12 55 25 55 25 2.2 = × × = = = The annual rate of interest as a decimal number is 2.2. To change this number to a percent, multiply the number by 100 and add a percent sign. Thus, the annual rate of interest paid is 220%. 7 Now try Exercise 29 MATHEMATICS TODAY Pawn Loans Since ancient times, pawnbroking has been a source of credit for people who cannot obtain loans from other financial institutions. A typical pawn transaction involves the customer presenting an item of value to a pawnbroker. The pawnbroker makes a loan to the customer based on a percentage of the value of the item. The pawnbroker keeps the item as collateral until the customer repays the loan plus the interest. If the customer defaults on the loan, the pawnbroker keeps the item and usually offers it for sale in his or her pawnshop. Because of the 15 to 20% default rate and the need to pay for retail space, pawn loans usually have a significantly higher rate of interest than other financial institutions (see Example 3 and Exercises 29 and 30). Why This Is Important Although pawn loans are generally easy to obtain, it is important to realize that a pawn loan will involve an extremely high interest rate— much higher than loan rates from other institutions. Example 4 Loan Choices for Farm Equipment Rodney needs to purchase new equipment for their farm but does not have the $1600 purchase price. The equipment dealership has two payment options. With option 1, Rodney can pay $800 as a down payment and then pay $850 in 6 months. With option 2, Rodney can pay $400 as a down payment and then pay $1380 in 9 months. Which option has a higher annual simple interest rate? Solution Before we compute the annual simple interest rates, we first need to compute the principle and the interest. Option 1 : To determine the principal of the loan, subtract the down payment from the purchase price of the equipment. Therefore, p $1600 $800 $800. = − = To determine the interest charged, subtract the purchase price of the equipment from the total amount paid. Therefore, i ($800 $850) $1600 $50. = + − = To determine the time, divide 6 by 12. Therefore t 0.5. 6 12 = = Then we use the simple interest formula. i p r t r r r r 50 800 0.5 50 400 50 400 0.125 = × × = × × = = = Option 1 has a 12.5% annual simple interest rate. Option 2 : The principal is p $1600 $400 $1200, = − = the interest is i ($400 $1380) $1600 $180, = + − = and the time is t 0.75. 9 12 = = Then i p r t = × × r 180 1200 0.75 = × × r 180 900 = r 180 900 = r 0.2 = Option 2 has a 20.0% annual simple interest rate. Therefore, option 2 charges a higher annual simple interest rate than option 1. 7 Now try Exercise 31 Steve Skjold/Shutterstock Mick Harper/Shutterstock
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