IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods
A deposit earns a nominal rate of interest of 8% per annum convertible quarterly. What is the equivalent effective annual rate of interest, to two decimal places?
The effective annual rate is 8.24%. A nominal 8% convertible quarterly gives 2% per quarter, and compounding for four quarters gives 1.02 to the power 4, which is 1.0824, so the effective annual rate is 8.24%.
- A8.00%
- B8.24%Correct
- C8.30%
- D8.16%
- 8.40%
Explanation
The quarterly effective rate is 8%/4 = 2%. The annual effective rate is 1.02^4 - 1 = 1.082432 - 1 = 8.24%. The 8.16% option comes from using half-yearly conversion, and 8.30% comes from monthly conversion.
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