Question $3$ A $$1,000,0003-$year term life insurance is sold to $(62)$ with benefits payable at the end of the year and premiums of $$6,300$ payable at the beginning of the year. Profit Test Basis: $7\%$ interest rate Pre$-$contract expenses of $$800$ plus $50\%$ of the first premium Renewal expenses of $10\%,$ including first year Standard ultimate survival model Reserve Basis: $6\%$ interest rate No expenses assumed $105\%$ of mortality rates of standard ultimate survival model Find the profit vector, profit signature, and profit margin with $10\%$ hurdle rate. Question $3$

A $\backslash (\backslash$$ $1,000,000\backslash )3-$year term life insurance is sold to $(62)$ with benefits payable at the end of the year and premiums of $\backslash (\backslash$$ $6,300\backslash )$ payable at the beginning of the year.

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|\}$

$\backslash$hline $\backslash$multirow$[$t$]\{4\}\{*\}\{$Profit Test Basis:$\}$ & $7\backslash \%$ interest rate $\backslash \backslash$

$\backslash$hline & Pre$-$contract expenses of $\backslash (\backslash$$ $800\backslash )$ plus $\backslash (50\backslash \%\backslash )$ of the first premium $\backslash \backslash$

$\backslash$hline & Renewal expenses of $10\backslash \%,$ including first year $\backslash \backslash$

$\backslash$hline & Standard ultimate survival model $\backslash \backslash$

$\backslash$hline $\backslash$multirow$[$t$]\{3\}\{*\}\{$Reserve Basis:$\}$ & $6\backslash \%$ interest rate $\backslash \backslash$

$\backslash$hline & No expenses assumed $\backslash \backslash$

$\backslash$hline & $105\backslash \%$ of mortality rates of standard ultimate survival model $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Find the profit vector, profit signature, and profit margin with $\backslash (10\backslash \%\backslash )$ hurdle rate.

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline $\backslash ($ q$\_\{62\}\backslash )$ & $0\mathrm{.}00423$ & $\backslash (\backslash$mathrm$\{$p$\}\_\{62\}\backslash )$ & $0\mathrm{.}99577$ & $\backslash$multicolumn$\{5\}\{|$c$|\}\{\backslash$multirow$\{3\}\{*\}\{\}\}\backslash \backslash$

$\backslash$hline $\backslash ($ q$\_\{63\}\backslash )$ & $0\mathrm{.}00473$ & $\backslash ($ p$\_\{63\}\backslash )$ & $0\mathrm{.}99527$ & & & & & $\backslash \backslash$

$\backslash$hline $\backslash ($ q$\_\{64\}\backslash )$ & $0\mathrm{.}00529$ & $\backslash (\backslash$mathrm$\{$p$\}\_\{64\}\backslash )$ & $0\mathrm{.}99471$ & & & & & $\backslash \backslash$

$\backslash$hline & $\backslash$multicolumn$\{3\}\{|$c$|\}\{$Beginning of Year$\}$ & $\backslash$multirow$[$b$]\{2\}\{*\}\{$Interest$\}$ & $\backslash$multicolumn$\{4\}\{|$c$|\}\{$End of Year$\}\backslash \backslash$

$\backslash$hline Year & Reserve & Premium & Expenses & & Benefits & Reserve & Profit Vector & Profit Signature $\backslash \backslash$

$\backslash$hline $0$ & & & & & & & & $\backslash \backslash$

$\backslash$hline $1$ & & & & & & & & $\backslash \backslash$

$\backslash$hline $2$ & & & & & & & & $\backslash \backslash$

$\backslash$hline $3$ & & & & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Profit Margin: $\backslash (\backslash$qquad $\backslash )$

Please show your work below