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

A sum of Rs 2,00,000 is payable in 4 years. The force of interest is constant at 5% per annum. What is its present value, to two decimal places in rupees?

With a constant force of interest of 5%, the discount factor over four years is e to the power minus 0.2, which is 0.818731. Multiplying by Rs 2,00,000 gives a present value of Rs 1,63,746.15. Simple interest would wrongly give a higher value.

  1. ARs 1,63,746.15Correct
  2. BRs 1,64,540.00
  3. CRs 1,66,666.67
  4. DRs 1,60,000.00
  5. Rs 1,62,000.00

Explanation

PV = 200000 × e^(-0.05×4) = 200000 × e^-0.2 = 200000 × 0.818731 = 1,63,746.15. Rs 1,66,666.67 comes from dividing by 1.2, treating 5% as simple interest.

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