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

The present value of Rs 1 due in n years is 0.7513 at an effective annual rate i. Which statement about the present value of Rs 1 due in 2n years at the same rate is correct?

The present value of Rs 1 due in 2n years is about 0.5645. At a constant rate the discount factor for 2n years is the square of the factor for n years, so 0.7513 squared gives 0.5645. Doubling or halving the factor is wrong.

  1. AIt equals 1.5026
  2. BIt equals 0.5645Correct
  3. CIt equals 0.3757
  4. DIt equals 0.2487
  5. It equals 0.6000

Explanation

Discount factors multiply over equal periods at a constant rate, so v^(2n) = (v^n)^2 = 0.7513^2 = 0.56445, about 0.5645. Doubling gives 1.5026 and halving gives 0.3757, both wrong.

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