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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Key assurance and annuity contracts

A life aged 55 buys a deferred annuity of ₹20,000 per annum, payable annually in advance from age 65 for life, funded by level annual premiums payable in advance for 10 years while alive. On the basis used, the present value of a deferred annuity-due of 1 per annum (deferred 10 years) is 7.20, and ä_{55:10} = 8.00. No benefit is payable on death in deferment and there are no expenses. What is the annual premium?

The annual premium is ₹18,000. Premiums are paid only during the 10-year deferment, so the premium annuity is ä_{55:10} = 8.00, and equating with the benefit value 20,000 × 7.20 = 1,44,000 gives 1,44,000 ÷ 8.

  1. A₹16,363.64
  2. B₹20,571.43
  3. C₹22,222.22
  4. D₹18,000.00Correct
  5. ₹14,400.00

Explanation

Equivalence principle: P × ä_{55:10} = 20,000 × 7.20 = 1,44,000. So P = 1,44,000 / 8.00 = ₹18,000. Inverting the ratio gives ₹22,222.22; using 7 or 8.8 as the annuity factor gives the other wrong figures.

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