IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
A nominal rate of interest of 12% per annum convertible monthly is quoted. What is the equivalent constant force of interest per annum, to four decimal places?
The equivalent force of interest is 0.1194. The monthly rate is 1%, so the annual accumulation factor is 1.01^12, and its natural logarithm equals 12 times ln 1.01, about 0.1194. Taking ln 1.12 wrongly treats 12% as an effective annual rate.
- A0.1200
- B0.1133
- C0.1268
- D0.1194Correct
- 0.0995
Explanation
The monthly effective rate is 1%, so 1+i = 1.01^12 and δ = ln(1+i) = 12 ln(1.01) = 12×0.0099503 = 0.1194. The option 0.1133 is ln(1.12), which wrongly treats 12% as an effective annual rate.
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