Question

You owe your best friend $2,700. Because you are short on cash, you offer to repay the loan over 10 months under the following condition. The first payment will be $90 at the end of month one. The second payment will be $90+ G at the end of month two. At the end of month three, you'll repay $90+2G. This pattern of increasing G amounts will continue for all remaining months. a. What is the value of G if the interest rate is 0.5% per month? b. What is the equivalent uniform monthly payment? c. Repeat Part (a) when the first payment is $110 (i.e., determine G).

Answer 1

a) P = [A1 + G(A/G, i, n)] * (P/A, i, n)

2700 = [90 + G(A/G, 0.5%, 10) * (P/A, 0.5%, 10)

2700 = [90 + G(4.4593)] * 9.7304

90 + 4.4593G = 2700 / 9.7304 = 277.48

4.4593G = 277.48 - 90 = 187.48

G = 187.48 / 4.4593 = 42

b) Equivalent uniform monthly payment = A1 + G(A/G, i, n)

                                                                = 90 + G(A/G, 0.5%, 10)

                                                                = 90 + 42(4.4593)

                                                                = 90 + 187.29

                                                                = 277.29

c) P = [A1 + G(A/G, i, n)] * (P/A, i, n)

2700 = [110 + G(A/G, 0.5%, 10) * (P/A, 0.5%, 10)

2700 = [110 + G(4.4593)] * 9.7304

110 + 4.4593G = 2700 / 9.7304 = 277.48

4.4593G = 277.48 - 110 = 167.48

G = 167.48 / 4.4593 = 37.56