question 12 April 2005 exam

I am not able to follow the solution given in the examiner's report for the question no.12 (ii) of april 2005 exam.
we are required to calculate the expected present value and the variance of the present value. But solution calculates the expected present value and the variance of the "expected present value".
Can anyone please clarify...

{Calculate the expected present value and variance of the present value of a term assurance of 1 payable immediately on death for a life aged 40 exact, if death occurs within 30 years.
Basis:
Interest 4% per annum
Mortality AM92 Select
Expenses: None}

 

dont sweat the litttle stuff

sure, the math ain't sound but its pretty close, if you use the answer in (i) and the substitute it in for the normal variance of a term insurance paid immediately you get..

var = i*/d* (Ax:n*) - {(i/d)(Ax:n)}^2 {if you can excuse the dels and missing 1's}
= (i^2+2i)/(2d) (Ax:n*) - {(i/d)(Ax:n)}^2
~=(i/d)^2 var(term assurance paid at the end of the year)

the approximation is sound for small i.

maybe they gave marks for both answers!