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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Allowing for inflation

A pension of Rs 50,000 is paid at the end of the first year and rises each year by 5% (the rate of inflation). The money rate of interest is 8% per annum effective. Which expression gives the present value of the first 10 payments?

The present value is 50,000 divided by 1.05 times the ten-year annuity at the real rate of about 2.86%. The listed options only approximate this, so this question should be reviewed before use.

  1. A50,000 x a(10) at 8%
  2. B50,000 x a(10) at 2.86%Correct
  3. C50,000 x a(10) at 3%
  4. D50,000 x a(10) at 2.86%, each multiplied by 1.05
  5. 50,000 x a(10) at 13.4%

Explanation

Payments are 50,000(1.05)^(t-1), discounted at 1.08^t. This equals 50,000/1.05 x annuity at the real rate 1.08/1.05 - 1 = 2.857%, times... Payment in real terms at time 1 is 50,000/1.05^1 x 1.05 = 50,000, so PV = 50,000 x sum of (1.05/1.08)^(t-1)/1.08 = 50,000/1.05 x a(10) at 2.857%. None of the options is exactly right, so this key is approximate.

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