Question

Earl obtained a loan for 15000 dollars. He will pay it back in 36 months with an interest rate of 14 yearly compounded monthly. Each payment will be $200 larger than the previous payment. Calculate the amount of the last payment.

Please show formulas and refrain from using excel. Thanks

Answer 1

P = $15000

n = 36 months

i = 14/12 = 1.16

G = 200

P = (A' + 200(A/G,1.16,36)(P/A,1.16,36)

15000 = [A' + 200(A/G,1.16,36)](P/A,1.16,36)

(A/G,1.16,36) = [(1/i) - [n / (1+i)^n - 1]] = [(1/0.0116) - [36 / (1+0.0116)^36 - 1]] = 1.2324

(P/A,1.16,36) = (1+i)^n - 1 / i * (1+i)^n = (1+0.0116)^36 - 1 / 0.0116 * (1+0.0116)^36 = 29.2922

15000 = [A' + 200(1.2324)](29.2922)

512.08 = A' + 246.48

A' = 265.6

The last payment = A' + 35G

The last payment = 265.6 + 35*200

The last payment = $7265.6