IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Practical applications of the equation of value (loans and APR)
A lender charges interest of 1.5% per month, compounded monthly, on a personal loan. What is the equivalent effective annual rate of interest?
The effective annual rate is 19.56%. Compound the monthly growth factor of 1.015 over twelve months to get 1.195618, then subtract one. The simple multiple of 18% understates the rate because it ignores compounding.
- A18.00%
- B19.25%
- C19.56%Correct
- D19.84%
- 21.00%
Explanation
The effective annual rate is 1.015^12 - 1 = 1.195618 - 1 = 19.56%. Simply multiplying 1.5% by 12 gives 18.00%, which ignores compounding. Treating 1.5% as a monthly discount rate gives 19.84%, which is also wrong.
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