IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
A deposit of Rs 1,000 earns interest at a constant force of interest of 6% per annum. What is the accumulated value after 5 years?
The accumulated value is Rs 1,349.86. With a constant force of interest of 6%, the accumulation factor over 5 years is e raised to 0.06 times 5, which is e^0.3 or about 1.3499. Using 1.06^5 wrongly treats the force as an effective rate.
- ARs 1,349.86Correct
- BRs 1,338.23
- CRs 1,300.00
- DRs 1,061.84
- Rs 1,419.07
Explanation
With constant force δ, the accumulation factor is e^(δt) = e^0.30 = 1.349859. So 1,000 grows to 1,349.86. Using 1.06^5 gives 1,338.23, which treats 6% as an effective annual rate instead of a force of interest.
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