QUESTION $1$PROBLEM # $1($Valuing an

Annuity$)$:You are working in the Human Resources department of a

large Canadian Corporation. One of your employees, Ted, will be

turning $60$ in one month$$s time and for health reasons, will be

taking early retirement from the company. Ted is planning on a

combination of company pension, RRSP investments, Canada Pension

Plan and Old Age Security to fund his retirement. Luckily, he has a

generous indexed company pension and significant RRSP investments

and does not need to count on Government pensions.Ted is unsure of how to handle his Canada Pension Plan

$($CPP$)$ entitlement. CPP provides a lifetime pension at retirement to

Canadians who have worked and paid into the plan. The dollar amount

of the pension depends on the individual's earnings and payments

into CPP during their working life. Ted has three

options:Option # $1$: Ted is entitled to a

monthly CPP payment of $$500$ which will start the month after he

turns $65.$Option # $2$: However, as an alternative

it is possible to start receiving CPP as early as one month after

turning $60,$ albeit at a reduced amount. The CPP payment is reduced

by $0\mathrm{.}6\%$ for every month before age $65$ to a maximum of

$36\%.$Option # $3$: Alternatively, he can wait

until age $70$ and get a higher monthly amount. If he starts to

receive CPP payments sometime after the age of $65,$ payments will

increase by $0\mathrm{.}7\%$ each month up to a maximum of $42\%$ at the age of

$70.$Payments will not increase after the age of

$70.$REQUIRED:Knowing that you are a whiz at financial matters, Ted

has come to you for advice on which option to choose. Assuming that

Ted will live to $85$ and can earn a $6\%$ return on his money. What is

your advice to Ted $-$ which option should he Choose?For each of the three $(3)$ options described above,

calculate the present value of the total Canada Pension Fund $($CPP$)$

payments. Make sure you clearly identify the values you are using

for interest rate $($r$),$ cash payment $($C$),$ and the number of payments

$($t$).$