Calculating Actuarial Present Value and Variance for Whole Life Insurance

[Jrb599]

Homework Statement

If delta(t) = 0.2/(1+0.05*t) and s(x)= 1-(x/100) for 0<x<100, calclulate
a. For a whole life insurance issued at age x, the actuarial present value and the variance of the present value of the benefits

Homework Equations

Present Value = Int(exp(-delta*t)) *Mu(t+x)*tPx

The Attempt at a Solution

I try to integrate the exponentional because the Mu and P can be pulled out but get a weird situation. Any thoughts or help?

 

[EnumaElish]

What's tPx?

 

[Jrb599]

s(x+t)/s(x)

For the Mu(x+t)*tPx you should get 1/(100-x)