Question

For loans with the same maturity, why would you care if they had different compounding periods? Explain how the effective annual rate (EFF%) can be used to solve this riddle.

Answer 1

As the interval for compounding decreases the effective annual rate increases, hence if a loan has smaller compounding period the effective annual period paid will be higher than for a bigger compounding period.

For example, a loan with a 12% interest compounded annually, effective annual rate will be 12%

However a 12% loan compounded semi annually will effectively cost, (1+0.12/2)^2-1=12.36% [(1+yearly rate/compounding period)^compounding periods-1].

This is because at the end of a compounding period the interest for the first compounding period is added to the value of loan and in the next compounding period interest is paid on the loan and the compounded interest for the first period and so on.