IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Practical applications of the equation of value (loans and APR)
A lender quotes a loan at a nominal rate of 12% per annum convertible monthly. What is the APR, expressed as an effective annual rate, to two decimal places?
The APR is 12.68%. A nominal 12% convertible monthly means 1% per month, and compounding that for twelve months gives 1.01^12 - 1, which is about 12.68% effective per year. This exceeds the nominal rate because interest is credited monthly.
- A12.00%
- B12.36%
- C12.68%Correct
- D12.75%
- 13.00%
Explanation
The monthly rate is 12%/12 = 1%. The effective annual rate is 1.01^12 - 1 = 1.126825 - 1 = 12.68%. The 12.00% option is the nominal rate. The 12.75% option wrongly uses continuous compounding, e^0.12 - 1. The 12.36% option wrongly uses half-yearly compounding.
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