IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross premiums and reserves
A 20-year endowment assurance has sum assured Rs 1,00,000. On the premium basis, A(x+10:10) = 0.6500 and the annuity-due value for 10 years is 8.00. The annual net premium is Rs 3,500. Using the prospective method, what is the net premium reserve at the end of year 10?
The reserve is Rs 37,000: the present value of future benefits is 0.65 x 1,00,000 = Rs 65,000, less the present value of future premiums 3,500 x 8 = Rs 28,000. Forgetting to subtract future premiums would give Rs 65,000.
- ARs 37,000Correct
- BRs 65,000
- CRs 28,000
- DRs 93,000
- Rs 9,000
Explanation
Reserve = 1,00,000 x 0.65 - 3,500 x 8.00 = 65,000 - 28,000 = 37,000. Rs 65,000 ignores the future premiums (the premium offset), while Rs 28,000 is just the premium annuity.
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