IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods
A bank quotes a nominal annual 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 four times gives 1.03 to the power 4, which equals 1.1255, so the effective annual rate is 12.55%.
- A12.00%
- B12.55%Correct
- C12.68%
- D12.75%
- 11.55%
Explanation
Quarterly rate = 12%/4 = 3%. Effective annual rate = 1.03^4 - 1 = 1.125509 - 1 = 12.55%. The 12.00% option ignores compounding within the year, and 12.68% corresponds to monthly compounding.
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