Suppose a $35-$year$-$old male plan member entered service at age $25.$ He has a

current salary of $$75,000$ and total past salary of $$650,000.$ Assume that salaries increase by

$2\mathrm{.}25\%$ per year. Suppose he retires at age $65.$

$1$

$($a$)$ Project his:

$($i$)$ final $5-$year average salary;

$($ii$)$ career average salary.

$($b$)$ Calculate his projected annual retirement income $($i$.$e$.,30$ years from now$)$ based on each

of the following pension formulas:

$($i$)65\%$ of the final $5-$year average salary;

$($ii$)2\mathrm{.}5\%$ of total career salary.

$($c$)$ Calculate the EPV of total retirement benefits in terms of a life annuity payable at the

beginning of each year $($without guarantee period$)$ for this member at his retirement date

with pension formulas $($i$)$ and $($ii$)$ in $($b$),$ respectively. Annuity functions are calculated

based on $2001$ CSO Mortality Table and i $=5\%$ per annum effective. You are given that

a$65=11\mathrm{.}21147.$

$($d$)$ Using the same EPV of total retirement benefits calculated in $($c$),$ find the new projected

annual retirement income if the life annuity comes with a $5-$year guarantee period, using

pension formulas $($i$)$ and $($ii$)$ in $($b$),$ respectively. Annuity functions are calculated based

on $2001$ CSO Mortality Table and i $=5\%$ per annum effective. You are given that

a$70=9\mathrm{.}64133.$