A life aged 40 purchases a 25 year endowment assurance contract. Level quarterly premiums are payable throughout the duration of the contract. The sum assured $100,000 is payable at maturity or at the end of the year of death. The quarterly premium, denoted by P, has been calculated using the following basis: Basis: Mortality: AM92 select Interest: 4% p.a. Initial expenses: $250 plus 60% of the gross annual premium Renewal expenses: 3% of the second and subsequent quarterly premiums Claims expenses: $500 on death; $100 on maturity. At age 60 , immediately before the premium then due, the life wishes to surrender the policy. The insurer calculates a surrender value equal to the gross retrospective policy value, assuming the above basis, but with 3% p.a. interest. Explain with reasons whether the surrender value would have been larger, the same or smaller than the above one if the office had used the prospective gross premium policy value assuming the above basis but (i) with 3% p.a. interest; (ii) with 4% p.a. interest Solution guide: Retrospectively: the lower interest rate values accumulated premium less benefits as if they had earned only 3% instead of the required 4%. Prospectively: the lower interest rate indicates a lower rate to be earned in the future. This implies that more reserves is required now in order to meet future liabilities. So the prospective reserve at 3%> the prospective reserve at 4%= the retrospective reserve at 4%> the retrospective reserve at 3%