PART $2$ Bonds and Investment Options

Jenna believes she could easily set aside $$3000$ of her $$40,000$ salary. She

is considering putting her savings in a stock fund. She just turned $22$ and has a

long way to go until retirement at age $65,$ and she considers this risk level

reasonable. The fund she is looking at has earned an average of $8\%$ over the past

$15$ years and could be expected to continue earning this amount, on average.

While she has no current retirement savings, five years ago Jenna's grandparents

gave her a new $30-$year U$.$S$.$ Treasury bond with a $$10,000$ face value.

Jenna wants to know her retirement income if she both $(1)$ sells her Treasury

bond at its current market value and invests the proceeds in the stock fund and

$(2)$ saves an additional $$4000$ at the end of each year in the stock fund from

now until she turns $65.$ Once she retires, Jenna wants those savings to last for

$25$ years until she is $90.$

Suppose Jenna's Treasury bond has a coupon interest rate of

$4\%,$ paid semiannually, while current Treasury bonds with the

same maturity date have a yield to maturity of $1\mathrm{.}3567\%$

$($expressed as an APR with semiannual compounding$).$ If she

has just received the bonds $10$ th coupon, for how much can

Jenna sell her treasury bond?

Suppose Jenna sells the bond, reinvests the proceeds, and then

saves as she planned. If$,$ indeed, Jenna earns an $8\%$ annual

return on her savings, how much could she withdraw each year in

retirement? $($Assume she begins withdrawing the money from the

account in equal amounts at the end of each year once her

retirement begins.$)$

Should Jenna sell her treasury bond and invest the proceeds in the stock

fund? Give one reason for and against the plan?

$***$ Would anyone know how to work this problem out $?$