IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
The force of interest at time t years is δ(t) = 0.02 + 0.004t. What is the accumulated value at time 5 of an investment of ₹10,000 made at time 0?
The accumulated value is ₹11,618.34. The accumulation factor is e raised to the integral of the force of interest. That integral is 0.02×5 + 0.002×25 = 0.15, so 10,000 × e^0.15 = 11,618.34.
- A₹11,051.71
- B₹11,274.97
- C₹11,500.00
- D₹11,618.34Correct
- ₹12,214.03
Explanation
The integral of δ(t) from 0 to 5 is 0.02×5 + 0.002×25 = 0.10 + 0.05 = 0.15. The accumulated value is 10,000 × e^0.15 = 11,618.34. Using only the constant 0.02 gives 11,051.71, which ignores the growth in δ.
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