IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Practical applications of the equation of value (loans and APR)
A Mumbai microfinance lender charges interest of 1.5% per month, compounded monthly, on a loan. What is the APR, expressed as an effective annual rate, to two decimal places?
The APR is 19.56% per annum. A monthly rate of 1.5% compounds twelve times a year, so the effective rate is 1.015 to the power 12 minus 1. Simply multiplying 1.5% by 12 gives 18%, which understates the true annual cost.
- A18.00%
- B19.56%Correct
- C19.86%
- D18.82%
- 21.62%
Explanation
The effective annual rate is 1.015^12 - 1 = 1.195618 - 1 = 19.56%. The 18.00% option multiplies the monthly rate by 12, which ignores compounding within the year.
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