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CCIII 7.1.2Have students turn their books to page pound InterestA common application of recursion and iteration is compound pound interest is interest tht is applied to previous interest as well as to the original amount of money borrowed or invested.The original amount of money is called the principalThe more often the interest is applied, that is, the more often it is compounded the faster the total amount of money (principal plus interest) grows.Thus the interest rate and compounding period are crucial factors in consumer loans, such as car loans and college loans.In the U.S., the Truth in Lending Act requires that lenders must report interest rates in a standard way.Using the Annual Percentage Rate (APR) consumers can more easily compare and understand loans.There are still problems with this calculationIt is common to advertise car loans with a stated APR. However, the interest is usually compounded monthly, not annually.Using the picture on p. 465The stated interest rate is 4.99%. Given the law about stating the APR, we will assume that this is an annual rate. The ad also implies that the loan will be computed monthly (“for up to 60 months”), so we will also assume that the interest will be compounded monthly. Finally, it is common to give the annual rate without adjusting for the effect of the monthly compounding. To carefully analyze this situation, we need to know the monthly interest rate.The monthly interest rate can be calculated as 112 of the annual rate.Suppose you borrow $10,000 to buy a used compact car at the interest rate shown in the ad. With repayment due in 48 monthly payments, you are told that your monthly payment will be $235. As a wise consumer, you should check to see if this payment amount is correct. Design a formula that models your principal over the time that you are making payments.Suppose someone offers you a “great deal” whereby you must pay only $40 per month until the loan is paid off. Describe what happens ot the repayment process in this situation. Is this such a great deal after all?P. 469Retirement is probably not something you are currently concerned about. However, working adults, even very young working adults, should have a financial plan for retirement. If you start saving early and take advantage of compound interest, then you should be in great financial shape by the time you retire. Consider twin sisters with different retirement savings plans.Cora begins a retirement account at age 20. She starts with $2,000 and then saves $2,000 per year at 7% interest, compounded annually, for 10 years. The she stops contributing to the account e keeps her savings invested at the same rate.Miranda does not save any money in her twenties. When she turns 30, she starts with $2,000 and then saves $2,000 per year at 7% interest, compounded annually for 35 years.Both sisters retire at age 65. Who do you think will have more retirement savings at ge 65? Test your conjecture by determining the amount of money saved by each sister at age 65. ................
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