Time Value of Money and Interest Rate Calculations

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1 Time Value of Money and Interest Rate Calculations Problem Set 2 0. A typical bank offers you a Visa credit card that charges interest on unpaid balance at 1.75% per month compounded monthly. This means that the nominal interest (annual percentage) rate for this account is A and the effective annual interest rate is B. Suppose your beginning balance was $600 and you make only the required minimum monthly payment (payable at the end of each month) of $20 for the next 3 months. If you made no new purchases with this card during this period, your unpaid balance (after your 3 rd payment) will be C at the end of 3 months. What are the values of A, B, and C? Nominal interest is the rate quoted based on an annual period. So, A= 1.75×12= 21%. B is Effective interest rate is the actual interest earned or paid in a year. I a = (1 + r/M) ^ M – 1 = [(1+0.21/12) ^12] - 1 = [1.0175^12] – 1 = 1.23 - 1 =0.23 = 23%. C is the unpaid balance at the end of three months, (Using the Brute force method.) Interest for the first month, = 1.75% × (600 - 20) = $ 10.15 Interest for the second month = 1.75% × (560+10.15) = $ 9.98 Interest for the third month = 1.75% × (540+10.15+9.98) = $ 9.80 Amount outstanding = 600 - 60+ (10.15+ 9.98+9.80) C = $540 + 29.93 =$ 569.93. 1. In January 1989, C&S, the largest mutual saving bank in Georgia, published the following information: interest, 7.55%; effective annual yield, 7.842%. The bank did not explain how the 7.55% is connected to the 7.842%, but you can figure out that the compounding scheme used by the bank should be I a = (1 + r/M)^M – 1 7.842 = (1+0.0755/M)^M - 1 1.07842=(1+0.0755/M)^M M= 12, the scheme is compounded monthly.
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