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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods

The force of interest at time t years is δ(t) = 0.02 + 0.01t. An investor deposits Rs 10,000 at time 0. What is the accumulated value at time 4 years, to two decimal places?

The accumulated value is Rs 11,735.11. The integral of the force of interest over four years is 0.16, since 0.02×4 is 0.08 and 0.005×16 is 0.08. Multiplying Rs 10,000 by e to the power 0.16 gives Rs 11,735.11.

  1. ARs 12,712.49
  2. BRs 10,832.87
  3. CRs 11,274.97
  4. DRs 11,735.11Correct
  5. Rs 11,600.00

Explanation

The integral of δ(t) from 0 to 4 is 0.02×4 + 0.005×16 = 0.08 + 0.08 = 0.16. The accumulated value is 10,000 × e^0.16 = 10,000 × 1.173511 = Rs 11,735.11. Using the end-point force 0.06 for four years gives Rs 12,712.49, which overstates the accumulation.

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