IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting
The effective annual rate of interest is 9%. Which of the following is the force of interest, to four decimal places?
The force of interest is 0.0862. It equals the natural logarithm of one plus the effective annual rate, so ln(1.09) = 0.08618, which rounds to 0.0862 and is below the effective rate of 9%.
- A0.0900
- B0.0862Correct
- C0.0844
- D0.0953
- 0.0827
Explanation
δ = ln(1.09) = 0.086178. Rounded to four decimals this is 0.0862. The 0.0900 option wrongly equates δ with i, and 0.0953 is ln(1.10).
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