April 07 - Ques 13 - Solution

[MindFull]

Hi guys, stuck again with one of the past paper solutions. In the answer, for the calculation of the Premium, it has 12P(0.95 * the annuity). My issue is shouldn't it be (12P - 0.05P)*the annuity? Can someone help me out>

Thanks alot.

 

[Mark Mitchell]

When valuing the EPV of the renewal expenses and renewal commission, we're told that these are (in total) 5% of the second and subsequent monthly premiums.

We can value this using an annuity payable monthly for the rest of the policyholder's life, but we need to subtract the very first payment (as no renewal expenses/commission are paid at time 0). We also need to remember that this annuity factor values a payment of 1/12 each month i.e. 1 per annum. Since the annual payment is 12P, we must have the multiplier as 12P (which gives a payment of P per month).

The reason your answer of (12P-0.05P)*annuity is wrong is that you've multiplied by P (the monthly premium) rather than 12P (the premium amount received over the whole year).

So:

EPV renewal expenses and commission = 0.05(12P*annuity - P)

We also have the EPV premiums = 12P*annuity, where the annuities are both the same (i.e. paid mothly etc)

EPV premiums - EPV exp/comm = 12P*annuity - 0.05*12P*annuity - 0.05P
= 12P(1-0.05)annuity - 0.05P

which is the answer given. (The 0.05P term gets added into the initial commission term.)

Hope this is clear.

M.

 

[MindFull]

Oh I see now.

Thanks much.