Question

5. For an annual interest rate of 10% compounded quarterly what it will be the effective annual interest rate?

Answer 1

Let r = Effective annual interest rate

For an annual rate i = 10% compunded quarterly (m=4) we need to find effective annual interest rate.

Let A = Principal amount invested, t = 1 year

For finding r, we need to find an interest rate r such that r being compounded annually gives the same future amount as 10% annually, compounded quarterly.

Hence;

A(1+i/m)^mt = A(1+r)^t

Hence by substituting values we get:

(1+ 0.1/4)⁴ = (1+r)

1.025⁴ = 1+r

1.1038 = 1 + r

r = 0.1038 = 10.38%

r = 10.38% = Effective annual interest rate