IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
The nominal rate of interest convertible quarterly is 8% per annum. What is the equivalent effective annual rate, to two decimal places?
The equivalent effective annual rate is 8.24%. Quarterly conversion gives 2% per quarter, and 1.02 raised to the fourth power is 1.0824. The 8.16% option is the semi-annual conversion result, and 8.00% ignores compounding.
- A8.00%
- B8.24%Correct
- C8.16%
- D8.32%
- 8.30%
Explanation
Effective rate = (1 + 0.08/4)^4 - 1 = 1.02^4 - 1 = 1.082432 - 1 = 8.24%. 8.00% ignores compounding. 8.16% is the half-yearly equivalent (1.04^2 - 1).
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