IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting
An investment earns a nominal rate of interest of 12% per annum convertible quarterly. What is the equivalent effective annual rate of interest, to two decimal places?
The effective annual rate is 12.55%. A nominal 12% convertible quarterly gives 3% per quarter, and compounding this over four quarters gives 1.03 to the power 4, which is 1.1255, so the annual effective rate is 12.55%.
- A12.00%
- B12.36%
- C12.55%Correct
- D12.68%
- 13.00%
Explanation
Quarterly rate = 12%/4 = 3%. Effective annual rate = 1.03^4 - 1 = 1.125509 - 1 = 12.55%. The 12.36% option is the semi-annual conversion (1.06^2 - 1), and 12.00% ignores compounding.
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