IAI Actuarial Core Principles · Business Finance · Key principles of finance
A bank quotes a nominal annual rate of 12% compounded quarterly on a deposit. What is the effective annual rate, to the nearest 0.01%? (1.03^4 = 1.125509)
The effective annual rate is 12.55%. The 12% nominal rate is split into four quarterly rates of 3%, and compounding them gives 1.03 to the power 4 minus 1, which is 12.55%. This exceeds 12% because interest is earned on interest within the year.
- A12.00%
- B12.55%Correct
- C12.68%
- D3.00%
- 12.36%
Explanation
Quarterly rate = 12%/4 = 3%. Effective annual rate = 1.03^4 − 1 = 12.5509%, i.e. 12.55%. 12.68% is the monthly compounding result, which does not apply. 12.00% ignores compounding.
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