Assume $Y$ is the present value of a $20-$year temporary life annuity of $$1$ payable at the beginning of each year as long as an individual aged $(x)$ is alive. You are additionally given the following assumptions:

$v=0\mathrm{.}95.$

${?}_{20}{q}_x=0\mathrm{.}2.$

$|)=0\mathrm{.}10.$

$|)=0\mathrm{.}15.$

What is the closest value to $E[Y^2]?$

$320$

$5$

$132$

$289$

$31$