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

A whole life policy with sum assured ₹1,00,000 was issued to a life aged x. Level annual premiums of ₹3,200 are payable in advance for 20 years only. At the end of year 10 the policyholder is alive. Net premium reserve basis: A_{x+10} = 0.45, ä_{x+10} = 13.0 and ä_{x+10:10} = 7.5. What is the net premium reserve at that time?

The reserve is ₹21,000. It is the value of the future benefit, 45,000, minus the value of the remaining ten years of premiums, 3,200 × 7.5 = 24,000. The whole life annuity factor must not be used because premiums cease at the end of year 20.

  1. A₹45,000.00
  2. B₹3,400.00
  3. C₹69,000.00
  4. D₹13,000.00
  5. ₹21,000.00Correct

Explanation

Future premiums run for only 10 more years. The reserve is 100000 × 0.45 − 3200 × 7.5 = 45,000 − 24,000 = ₹21,000. Using ä_{x+10} = 13 gives 45,000 − 41,600 = ₹3,400, which wrongly assumes premiums continue for life. Adding the premium value gives ₹69,000. Using 10 as the annuity factor gives ₹13,000.

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