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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Financial instruments and insurance contracts as cashflow models

A perpetuity pays ₹12,000 at the end of each year, forever. The effective annual rate of interest is 8%. A second arrangement pays ₹12,000 at the start of each year, forever, at the same rate. What is the difference between the present value of the second arrangement and the first?

The difference is ₹12,000. The beginning-of-year perpetuity is worth ₹1,62,000 against ₹1,50,000 for the end-of-year perpetuity, because it includes one extra payment of ₹12,000 made immediately, and all later payments are identical in timing.

  1. A₹12,000Correct
  2. B₹1,50,000
  3. C₹96,000
  4. D₹1,62,000
  5. ₹8,000

Explanation

First PV = 12000/0.08 = 1,50,000. Second PV = 12000 x (1.08/0.08) = 1,62,000. Difference = 12,000, which is the payment received immediately at time 0. The figure ₹96,000 arises from multiplying 12,000 by 8.

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