Question

A 5-year loan of 500,000 with an annual effective discount rate of 8% is to be repaid by level end-of-year payments. If the first four payments had been rounded up to the next multiple of 1,000, the final payment would be X. Calculate X.

a. 103,500
b. 111,700
c. 115,200
d. 125,200
e. 127,500

Answer 1

125,200

Explanation:

Given :

Loan amount (P) = 500,000

Annual effective interest (r) = 8% = 8/100 = 0.08

n = 5 (5th payment) = final payment

Using the relation :

Payment amount per period :

A = (P(1 + r)^n * r) ÷ (1 + r)^n - 1

A = (500000(1 + 0.08)^5 * 0.08) / (1 + 0.08)^5 - 1

A = 40000(1.08)^5 / 1.08^5 - 1

A = 40000(1.4693280768) / 1.4693280768 - 1

A = 58773.123072 / 0.4693280768

A = 125228.22

A = 125,200 ( nearest hundred)