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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross premiums and reserves

A policy has a policy value of ₹20,000 at the start of year 6, before the premium and expense for that year. The gross premium of ₹5,000 is paid at the start of the year, with an expense of ₹200 incurred at the same time. The death benefit of ₹100,000 is paid at the end of the year of death. The mortality rate is 0.01 and the interest rate is 6% per year. Using the recursive relationship with policy values, what is the policy value at the end of year 6, for a surviving policyholder?

The policy value is ₹25,543.43. Accumulate (20,000 + 5,000 − 200) at 6% to get 26,288, deduct the expected death outgo of 1,000 to get 25,288, then divide by the survival probability 0.99. Ignoring the ₹200 expense would overstate the value.

  1. A₹25,543.43Correct
  2. B₹25,757.58
  3. C₹25,288.00
  4. D₹26,553.54
  5. ₹25,555.56

Explanation

(20,000 + 5,000 − 200)(1.06) = 26,288. Subtract the expected death cost 0.01 × 100,000 = 1,000 to get 25,288. Divide by p = 0.99 to get ₹25,543.43. Ignoring the expense gives 25,757.58. Failing to deduct the death cost gives 26,553.54. Taking off the expense after interest gives 25,555.56.

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