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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions

Rs 80,000 is due in 3 years. Using a constant effective annual discount rate d = 5%, what is its present value?

The present value is Rs 68,590. With a constant effective discount rate of 5%, each year multiplies by 0.95, so the value is 80,000 times 0.95 cubed, which is 0.857375, giving Rs 68,590.

  1. ARs 68,590Correct
  2. BRs 69,000
  3. CRs 70,400
  4. DRs 72,000
  5. Rs 67,200

Explanation

With effective discount d, v = 1 - d = 0.95. PV = 80000 × 0.95^3 = 80000 × 0.857375 = Rs 68,590. Using 1 - 3d = 0.85 gives Rs 68,000 (simple discount), which is a different basis, and 1/1.05^3 gives Rs 69,107.

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