IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
The force of interest at time t (in years) is δ(t) = 0.02 + 0.004t. What is the present value of a payment of Rs 10,000 due at time 5?
The present value is Rs 8,607.08. Integrate the force of interest from 0 to 5 to get 0.15, then discount by e^(-0.15). Applying the time-5 force of 0.04 over the whole period overstates the discount.
- ARs 8,187.31
- BRs 8,607.08Correct
- CRs 9,048.37
- DRs 11,618.34
- Rs 8,219.27
Explanation
The integral of δ from 0 to 5 is 0.02×5 + 0.004×25/2 = 0.10 + 0.05 = 0.15. The present value is 10,000e^(-0.15) = 8,607.08. Using δ(5)=0.04 for the whole period gives e^(-0.2), which is 8,187.31 and is wrong because it ignores the changing force.
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