Question

You are given a loan on which interest is charged over a 3-year period, as follows:

(i) an effective rate of discount of 9% for the first year;

(ii) a nominal rate of interest of 6% compounded semiannually for the second year; and

(iii) a force of interest of 5% for the third year.

Calculate the annual effective rate of interest over the 3-year period to the closest value.

Answer 1

First year annual interest rate = 9% or 0.09

Second year annual interest rate = 6%*2half years = 12% or 0.12

Third year annual interest rate = 5% or 0.05

Let 'r' be the annual effective interest rate.

Annual Effective rate of interest over the 3-year period is :

=> (1+r)^3 = (1+i(1)) * (1+i(2)) * (1+i(3))

=> (1+r) = Cube root of ((1+0.09) * (1+0.12) * (1+0.05))

=> (1+r) = Cube root of (1.28184)

=> (1+r) = 1.0863

=> r = 1.0863 - 1

Therefore, effective annual interest rate is 0.0863 or 8.63%