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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Financial instruments and insurance contracts as cashflow models

A life aged x buys a 2-year pure endowment that pays Rs 1,00,000 at the end of 2 years only if the life survives. The probability of surviving 2 years is 0.90 and the effective annual interest rate is 5%. What is the expected present value of the benefit at issue?

The expected present value is Rs 81,632.65. The payment is made only if the life survives two years, so Rs 1,00,000 is multiplied by the survival probability 0.90 and discounted for two years at 5%, giving 90,000 divided by 1.1025.

  1. ARs 90,000.00
  2. BRs 90,702.95
  3. CRs 85,714.29
  4. DRs 81,632.65Correct
  5. Rs 99,225.00

Explanation

The benefit is paid only on survival, so EPV = 1,00,000 × 0.90 × v^2 = 90,000/1.1025 = Rs 81,632.65. Rs 90,000 omits discounting. Rs 90,702.95 discounts but ignores the survival probability. Rs 85,714.29 discounts for only one year. Rs 99,225 multiplies by 1.05^2 instead of discounting.

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