$$ Actuarial Science Do not copy others or else THUMB DOWN! An $80-$year$-$old elects to purchase a $10-$year temporary annuity from an insurance

company paying $$5,000$ quarterly, with payments made at the beginning of each

quarter.

The insurance company uses the $3-$term Woolhouse formula for calculating $m-$thly

annuities and the interest rate is $4\%.$

You are given the following:

$A_{79}=0\mathrm{.}52$

$A_{90}=0\mathrm{.}65$

$l_{79+t}=10,000-25t^2$

Calculate the expected present value of this annuity.