1Time Value of Money and Interest Rate CalculationsProblem Set 20.A typical bank offers you a Visa credit card that charges interest on unpaid balance at1.75%per month compounded monthly. This means that the nominal interest (annualpercentage) rate for this account is A and the effective annual interest rate is B. Supposeyour beginning balance was $600 and you make only the required minimummonthlypayment (payable at the end of each month) of $20 for the next 3 months. If you made nonew purchases with this card during this period, your unpaid balance (after your 3rdpayment) 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 isEffective 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)=$10.15Interest for the second month=1.75% × (560+10.15) = $ 9.98Interest for the third month= 1.75% × (540+10.15+9.98) = $9.80Amount outstanding= 600-60+ (10.15+9.98+9.80)C = $540 + 29.93 =$ 569.93.1.In January 1989, C&S, thelargest mutual saving bank in Georgia, published the followinginformation: interest, 7.55%; effective annual yield, 7.842%. The bank did not explain howthe 7.55% is connected to the 7.842%, but you can figure out that the compounding schemeused by the bank should beI a = (1 + r/M)^M–17.842 = (1+0.0755/M)^M-11.07842=(1+0.0755/M)^MM= 12, the scheme is compounded monthly.Preview Mode
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