A loan of S2,500 for a new, high-end laptop computer is to be repaid in 13 end-o

Question

A loan of S2,500 for a new, high-end laptop computer is to be repaid in 13 end-of-month payments (starting one month from now). The monthly payments are determined as follows Loan principal Interest for 13 months at 1.6% per month Loan application fee Total Monthly payment S3,114.93/13 $239.61 $2,500 520.00 94.93 $3,114.93 What nominal and effective interest rates per year are actually being paid? Hint: Draw a cash-flow diagram from the perspective of the lender 14 S2,500 S2,500 1"--"f-S23901 --2----5-$239.61 2 13 14 12 13 $2,500 The nominal interest rate is % per year. (Round to one decimal place.)

Explanation / Answer

The cash flow diagram that is relevant to the given problem is the cash flow diagram of "B". From the perspective of the lender the initial loan of $2500 is a cash outflow for it and then the monthly payments of $239.61 are cash inflows. There will be 13 monthly inflows for the lender.

Nominal interest rate per year = 1.6%*12 months = 19.2%

Total interest and fee = 520+94.93 = 614.93

Interest and fee for 12 months = 614.93/13*12 = 567.63

Effective interest rate per year = 567.63/2500 = 22.7%

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