Question

1.349 120 00555 5492 00305 745 mm 2) Amotorcycle is for sale for $26,000. The dealer is willing to sell on the following terms: No down payment, pay $ 440 at the end of each of the firs four months; pay $ 840 at the end of each month after until the loan has been fully repaid. 840 At an interest rate of 12% annual interest rate compounded monthly, how many payments will be required?

Answer 1

(P/A, i,n) = ((1 + i)^n-1)/(i(1 + i)^n)

i = 12% = 12% / 12 = 1% per month

Let the no. of months be n for 840 payments, then

26000 = 440 * (P/A, 1%,4) + 840 * (P/A, 1%,n) * (P/F, 1%,4)

26000 = 440 * 3.901966 + 840 * (P/A, 1%,n) * 0.960980

840 * (P/A, 1%,n) * 0.960980 = 26000 - 440 * 3.901966 = 24283.135

(P/A, 1%,n) = 24283.135 / (840 * 0.960980 ) = 30.08230

Using formula for (P/A, 1%,n)

((1 + 0.01)^n-1)/(0.01 * (1 + 0.01)^n) = 30.08230

((1.01)^n - 1)/(0.01 * (1.01)^n) = 30.08230

(1.01)^n - 1 = 30.08230 * 0.01 * (1.01)^n

(1.01)^n - 1 = 0.300823 * (1.01)^n

(1.01)^n = 1 / (1 - 0.300823 ) = 1.430252997

taking log both sides

n = log 1.430252997 / log 1.01 = 35.96 months

n = 35.96 months ~ 36 months (Approx)