The short question is extracted from page 92 of SP2 combined material pack, chapter 3 Life Insurance Product (3) under section 1.3 Capital requirement for Immediate Annuity. Original question is pasted as green while answer is pasted as blue in below. I have change the content to red fond to ease reference for my queries. Queries: 1) In calculating reserve, why do we need to multiply a factor of (12.85/11.39) whereby 12.85 is mortality rate under valuation basis while 11.39 is mortality rate under premium basis? With respect to first question above, isn't reserve should be net cashflow*probability of surviving as at end of first year = (100-5)*(1-12.85/100) = 82.7925? 3) the interest rate 5.5% and 4% in pricing and reserve basis were not being used. Is it because the question is about the initial capital strain which is concerning on the first year cashflow only? 4) If question is changed to consider the asset share in second year where renewal expense is included, how should we apply the interest rate, should we use 5.5% or 4%? Original question A life insurance company sells an immediate annuity assuming initial commission and expenses of 5% of single premium. (Renewal expenses are ignored.) The interest rate used for pricing is 5.5% pa. At this rate, a life annuity of 1 pa using the premium basis mortality is 11.39 for the policyholder concerned. The insurance company is required to reserve at a valuation interest rate of 4% pa. The life annuity for the policyholder at this rate of interest and using the valuation mortality basis is 12.85. The insurance company is also required to hold solvency capital of 4% of reserves. On sale, the commission and expenses were equal to those assumed in the pricing basis. Calculate the capital strain on the sale as a percentage of the single premium. Answer Answer: 16.5% This is derived by considering all of the cashflow components and reserving / solvency capital requirements, as shown below. For a premium of 100: Positives: Premium = 100 Negatives: Commission and expenses = 5 Setting up reserve = 107.2 Required solvency capital = 4.3 Total = -16.5 where the reserve is derived as (100 – 5) × 12.85 / 11.39 = 107.2 and the solvency capital is derived as 107.2 × 4% = 4.3. So what does this mean? If the life insurance company wants to sell £100 million of such policies this year, it will require £16.5 million to finance those sales. Therefore the difference between the pricing and the reserving bases costs 12.2% (from 107.2 minus 95) – although we should bear in mind that these numbers are entirely artificial.