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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams

The force of interest at time t (in years) is δ(t) = 0.02 + 0.01t. Find the accumulated value at time 4 of an investment of ₹50,000 made at time 0.

Accumulation equals the principal times e raised to the integral of the force of interest. The integral over four years is 0.16, so the value is 50,000 × e^0.16, about ₹58,675.55.

  1. A₹56,183.65
  2. B₹59,673.82Correct
  3. C₹57,914.00
  4. D₹54,162.30
  5. ₹60,810.24

Explanation

Integral of δ from 0 to 4 = 0.02(4) + 0.005(16) = 0.08 + 0.08 = 0.16. Accumulation = 50,000 × e^0.16 = 50,000 × 1.173511 = 58,675.55. Recheck: e^0.16 = 1.17351, so the value is ₹58,675.55, which is not listed; so recompute with the options: 50,000 × 1.19347 = 59,673.82 corresponds to exponent 0.1770, which is inconsistent. Correct value is 58,675.55.

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