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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting

The force of interest is a constant 5% per annum. What is the present value of Rs 2,00,000 payable in 3 years, to the nearest rupee?

The present value is about Rs 1,72,142. With a constant force of interest of 5%, the discount factor over three years is e to the power minus 0.15, which is 0.8607, and multiplying by Rs 2,00,000 gives the answer.

  1. ARs 1,72,142Correct
  2. BRs 1,72,500
  3. CRs 1,70,000
  4. DRs 1,76,190
  5. Rs 2,32,368

Explanation

PV = 200000 × e^-0.15. e^-0.15 = 0.860708, so PV = 172,142. Rs 1,70,000 uses simple discounting at 5% for 3 years (a 15% deduction). Rs 1,72,500 results from treating the 5% as discount rate on a different base. Rs 1,76,190 is 200000/1.05^3 ... wrongly treating force as effective rate.

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