A certain sum of money is lent at a compound interest rate of 10% per annum payable half yearly. What is the effective annual rate of interest?

The effective annual rate is 10.25%.

10% per year compounded half yearly means 5% per half year.

Growth in one year = (1 + 5/100)^2 = 1.1025.

Effective rate = 1.1025 - 1 = 0.1025.

0.1025 = 10.25%.