2011 April Past paper - Q11

[tsubasakel]

Hello,

I would like to ask how to calculate the extra death benefit, extra surrender benefit, extra maturity benefit and the end year cashflow in April 2011 past paper question 11 part (ii), as I cannot work these out as the solution.

Thanks for your help.

Kelvin

 

[Polz87]

The death benefit is guaranteed at 10,000, which means that if the end year unit fund value (after charges) is under this the difference must come from the non unit fund and the cost will be

dependent probability of death * (10,000 - fund value)

If someone surrenders then they get payed the surrender benefits defined in the question (the different multiples of premiums payed to date). This will come out of the unit fund and out of the non unit fund if greater than the unit fund value. The profit/loss on surrender is then

dependent probability of surrender * (fund value - surrender benefit)

because if the surrender benefit is less than the fund value then the company makes a profit of the difference.

Finally the maturity benefit is 1.05 x unit fund value, which means that
0.05*fund value will have to come out of the non unit fund. The maturity cost is then

(ap)_64 * 0.05*final unit fund value

where (ap)_64 = 1- (aq)_64^d - (aq)_64^s

which is the probability of a policy which was in force at the beginning of the final year still being in force at the end of the contract and therefore entitled to the maturity benefit