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

A perpetuity-immediate pays Rs 2,000 per year. Another perpetuity-immediate pays Rs X at the end of every second year (times 2, 4, 6, ...). At an effective annual rate of 10%, both have equal present value. What is X?

X is Rs 4,200. The annual perpetuity is worth 20,000, and a perpetuity paying every two years is worth X divided by the two-year rate of 0.21. Equating gives X as 20,000 times 0.21, which is 4,200.

  1. ARs 4,000.00
  2. BRs 4,200.00Correct
  3. CRs 4,400.00
  4. DRs 2,200.00
  5. Rs 3,800.00

Explanation

First PV = 2,000/0.10 = 20,000. Second PV = X/((1.1)^2 - 1) = X/0.21. Setting equal gives X = 20,000 x 0.21 = Rs 4,200. Rs 4,000 would ignore interest on the delayed payment.

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