10.3 Compound Interest 605 finance charge. In essence, the customer is borrowing the money (the refund minus the finance charge) from the tax preparer, prepaying the interest (as in a discount note), and then repaying the loan with the tax refund. This procedure allows customers access to their tax refund money without having to wait. Joy had a tax refund of $743.21 due. She was able to get her tax refund immediately by paying a finance charge of $39.95. What annual simple interest rate, to the nearest hundredth of a percent, is Joy paying for this loan assuming a) the tax refund check would be available in 5 days? 409.01% b) the tax refund check would be available in 10 days? 204.50% c) the tax refund check would be available in 20 days? 102.25% 64. Prime Interest Rate Nick borrowed $600 for 3 months. The banker said that Nick must repay the loan at the rate of $200 per month plus interest. The bank was charging a rate of 2 percentage points above the prime interest rate. The prime interest rate is the rate charged to preferred customers of the bank. During the first month the prime interest rate was 4.75% during the second month it was 5% and during the third month it was 5.25% a) Determine the amount Nick paid the bank at the end of the first month, at the end of the second month, and at the end of the third month. $203.38 first month; $202.33 second month; $201.21 third month b) What was the total amount of interest Nick paid the bank? $6.92 65. Banker’s Rule The Banker’s rule considers a year to have 360 instead of 365 days. This exercise highlights the advantage the Banker’s rule provides to banks and other lenders. Professor Acks obtains a bank loan to open a health food store. She borrows $25,000 for 180 days and pays a 3% simple interest rate on the loan. a) Using the Banker’s rule and t , 180 360 = calculate the simple interest Professor Acks pays on this loan. $375 b) Next, calculate the simple interest Professor Acks would pay on this loan if the simple interest were calculated using t 180 365 = instead. $369.86 c) How much more simple interest does the bank receive by using a denominator of 360 rather than 365? $5.14 d) Determine the percent increase in simple interest the bank receives by using a denominator of 360 rather than 365 by dividing the answer to part (c) by the answer to part (b). Round your answer to the nearest hundredth of a percent. 1.39% Recreational Mathematics 66. Columbus Investment On August 3, 1492, Christopher Columbus set sail on a voyage that would eventually lead him to the Americas. If on this day Columbus had invested $1 in a 5% simple interest account, determine the amount of interest the account would have earned by the following dates. Use a scientific calculator and disregard leap years in your calculations. a) December 11, 1620 (Pilgrims land on Plymouth Rock) $6.42 b) July 4, 1776 (Declaration of Independence) $14.20 c) December 7, 1941 (United States enters World War II) $22.47 d) Today’s date Answers will vary. Research Activity 67. Loan Sources Consider the following places where a loan may be obtained: banks, savings and loans, credit unions, and pawnshops. Write a report that includes the following information: a) Describe the ownership of each. b) Historically, what need is each fulfilling? c) What are the advantages and disadvantages of obtaining a loan from each of those places listed? Albert Einstein said of compound interest, “The most powerful force in the universe is compound interest.” What is this marvelous concept that warrants such a strong statement from one of the most intelligent human beings of all time? Another very intelligent person, Benjamin Franklin, described compound interest quite well when he said, “Money makes money and the money that money makes makes more money.” In this section, we will introduce compound interest. Compound Interest SECTION 10.3 LEARNING GOALS Upon completion of this section, you will be able to: 7 Solve problems involving compound interest. 7 Solve problems involving the present value of an investment. Lyudmyla Kharlamova/ Shutterstock
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