Question

Suppose that $30,000 is borrowed today at 12% interest. The loan is to be repaid by uniform annual payments for 5 years, beginning 1 year from now. Calculate the annual payment. Select one: o a. A = P (A/P,12%,5) = $30,000 (0.2774) = $8,322 per year b. A = P (A/P,12%,60) = $30,000 (0.1201) = $3603.00 per year O C. A = P/n = $30,000 / 60 years = $500 per year d. P = A (P/A,12%,5) = $30,000 ($3.6048)= $108,140 per year

Answer 1

Answer

We want to calculate periodic payment such that present value of all future payment made is equal to the amount borrowed.

Thus formula for A = P(A/P,i,n) we have to calculate annual amount and thus n = number of years = 5, i = interest rate = 12%.

Thus A = P(A/P,12%,5). here P = 30,000 and using compound interest table, P(A/P,12%,5) = 0.2774

=> A = 30,000*0.2774 = 8322

Hence, the correct answer is (a) A = P(A/P,12%,5) = $30,000(0.2774) = $8322

{Another way :

Note :

P = (A/i)(1 - 1/(1 + i)n) where P = 30,000, n = 5, i = 12% = 0.12 and using this you can calculate A}