Question

please no excel only formulas

4. Tim got a new car with a loan of $23,000 at 6% per year compounded monthly. There are 35 payments. If each payment is larger than the previous one by $17.00. What would be the size of first and last payment?

Answer 1

i = 6% / 12 = 0.5% per month

t = 35 months

G = 17

As per given condition

23000 = A *(P/A,0.5%,35) + 17 * (P/G,0.5%,35)

23000 = A *((1 + 0.005)^35-1)/(0.005 * (1 + 0.005)^35) + 17 * {((1 + 0.005)^35 -1)/((0.005^2)(1 + 0.005)^35) - 35/(0.005 * ((1 + 0.005)^35))}

23000 = A *((1.005)^35-1)/(0.005 * (1.005)^35) + 17 * {((1.005)^35 -1)/((0.005^2)(1.005)^35) - 35/(0.005 * ((1.005)^35))}

23000 = A * 32.035371 + 17 * 528.312260

A = (23000 - 17 * 528.312260) / 32.035371 = 14018.69 / 32.035371 = 437.60

Pls comment if you think final solution is wrong or you require further explanation