Question

A loan is being repaid by quarterly installments of 2000 at the end of each quarter at 12.9% convertible quarterly. If the loan balance at the end of the third year is $18085.19, find the original loan amount. A. 32000

B. 45714
C. 51200
D. 26667
E. 56000

Answer 1

The original loan amount is calculated using the present value formula for annuities, taking into account the quarterly payments, interest rate, and the balance at the end of the third year.

Step-by-step explanation:

The student is asked to find the original loan amount given that a loan is being repaid with quarterly installments of $2000 at 12.9% interest convertible quarterly, and the loan balance at the end of the third year is $18085.19. To find the original loan amount, we can use the present value formula for an annuity:

Let L be the original loan amount. The loan balance after 3 years is the present value of the remaining payments, so we have:

L - PV of 12 payments = PV of the remaining payments (which is $18085.19).
L = $18085.19 + PV of 12 payments.
The present value of 12 quarterly payments of $2000 can be calculated using the present value of annuity formula
`PV = R [1 - (1 + i)^(-n)] / i`, where R is the regular payment, i is the interest rate per period and n is the number of periods. Substituting R = $2000, i = 0.129/4 (quarterly interest rate), and n = 12 (payments for 3 years), we find the present value of the 12 payments, then add that to $18085.19 to determine L.