IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods
The effective annual rate of interest is 8%. What is the equivalent constant force of interest per annum, to two decimal places as a percentage?
The equivalent force of interest is 7.70% per annum. It is found as δ = ln(1.08) = 0.07696. The force of interest is always below the effective annual rate for positive rates, so 8% cannot be right, and 7.41% is the discount rate.
- A7.70%Correct
- B8.00%
- C7.41%
- D8.33%
- 7.85%
Explanation
δ = ln(1+i) = ln(1.08) = 0.076961, which is 7.70%. The 8.00% option wrongly takes δ equal to i. The 7.41% option is the discount rate d = 0.08/1.08, which is a different quantity. The 8.33% option is i/(1−i), which is also wrong.
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