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

A two-year with-profits endowment was bought for a single premium. Sum assured is Rs 100,000. A reversionary bonus of Rs 5,000 was declared at the end of year 1 and is payable with the sum assured on death in year 2 or on maturity at the end of year 2. No further bonuses will be declared. Death benefits are paid at the end of the year of death. Using i = 5% p.a. and q = 0.02 for the year, what is the reserve at the end of year 1, to two decimal places?

The reserve is Rs 100,000.00. Both the death benefit and the maturity benefit equal the sum assured plus the declared bonus, Rs 105,000, paid at the end of year 2. Discounting one year at 5% gives 105,000/1.05. Leaving out the vested bonus would understate the reserve.

  1. ARs 95,238.10
  2. BRs 105,000.00
  3. CRs 100,000.00Correct
  4. DRs 102,000.00
  5. Rs 99,047.62

Explanation

Whether the policyholder dies in year 2 or survives, Rs 105,000 (sum assured plus bonus) is paid at time 2, so the reserve is 105,000 × v = 105,000/1.05 = Rs 100,000.00. Omitting the declared bonus gives 95,238.10, which is wrong because the bonus is already vested.

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