Question

What nominal rate per annum compounded weekly is equal to 9.5% p.a. compounded semi-annually?

Answer 1

n1 = 52 weeks

n2 = 2 semi annual compoundings

Let APR1 = Nominal interest rate

APR2 = 9.5%

[1 + (APR1 / n1)]^n1 - 1 = [1 + (APR2 / n2)]^n2 - 1

[1 + (APR1 / 52)]^52 -1 = [1 + (9.5%/2)]^2 -1

[1 + (APR1 / 52)]^52 = 1.09725625

1 + (APR1 / 52) = 1.00178645

(APR1 / 52) = 0.00178645

APR1 = 0.0928954

Therefore, Nominal rate of 9.29% compounded weekly equal to 9.50% compounded semi annually