In the solution, EPV of benefits include a term + 10,00,000 * (1/1.019231) * v^15 * 15p50 * (1.019231^16 - 1.019231^15) (All at 6%). I am not able to understand, why was this term is added in benefits. Please explain.
(In my explanation I will use 1+b for 1.0192308.) This is just a piece of mathematical manipulation. They want to change the first expression for the EPV to be in the form of a full endowment assurance, with end of year of death payments, calculated at 4% interest. The powers of (1+b) therefore all need increasing by 1, except for the survival benefit, which already has the appropriate factor of (1+b)^15. So, first, multiply and divide the expression by (1+b), so that we have [1/(1+b)] outside the bracket. This makes the terms inside the bracket add up to be an endowment assurance at 4% except the maturity benefit. The maturity benefit is equal to [1/(1+b)] x [ (1+b)^16 * v15 * 15p50], whereas they need it to be [1/(1+b)] x [ (1+b)^15 * v15 * 15p50]. In order to make it work, therefore, they force the value to be [1/(1+b)] x [ (1+b)^15 * v15 * 15p50] and then add back the difference between this and the correct value of [1/(1+b)] x [ (1+b)^16 * v15 * 15p50] at the end to make it right again. It is this difference that is equal to the last term in the expression.
