IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
A deposit account quotes a nominal rate of 12% per annum convertible quarterly. What is the 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 about 1.1255. Subtracting 1 leaves 12.55%, above the 12% nominal rate.
- A12.00%
- B12.55%Correct
- C12.68%
- D13.00%
- 12.36%
Explanation
The quarterly rate is 12%/4 = 3%. The effective annual rate is 1.03^4 - 1 = 1.125509 - 1 = 12.55%. The 12.68% option comes from wrongly using monthly compounding, and 12.36% comes from using half-yearly compounding.
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