PLEASE MAKE SURE TO DRAW A TIME LINE.. THATS SOEMTHING I RLLY NEED PLS

PLP Industries wishes to accumulate funds to provide a retirement annuity for its vice$-$president

of research, Jane Magnan. Ms$.$ Magnan will retire in exactly $12$ years$$ time. Upon retirement, she

is entitled to receive an annual end$-$of$-$year payment of $$52,000$ for $20$ years. During the $12-$year

$$accumulation period,$$ PLP wishes to fund the annuity by making equal annual end$-$of$-$year

deposits into an account earning a return of $9\mathrm{.}64$ percent compounded quarterly. Once the $20-$year

$$retirement period$$ begins, PLP plans to move the accumulated monies into a safer investment

account that is expected to earn $7$ percent per year. At the end of the $20-$year retirement period, the

account balance will equal zero. Note that the first deposit will be made at the end of year $1$ and

the first distribution payment will be received at the end of year $13.$

a$)$ How large a sum must PLP accumulate by the end of year $12$ to provide the $20-$year,

$$52,000$ annuity? $(4$ points$)$

b$)$ If the interest rate was $7$ percent compounded monthly $($but everything else is the same$)$

would your answer in $($a$)$ be larger or smaller? Why? Note: you do not need calculations

for this answer. $(2$ points$)$

c$)$ How large must PLP$$s equal annual end$-$of$-$year investments into the account be over the

$12-$year accumulation period to fund fully Ms$.$ Magnan$$s retirement annuity? $(4$ points$)$

d$)$ How much would PLP have to invest annually during the accumulation period if Ms$.$

Magnan$$s retirement annuity was a perpetuity and all other terms were the same as initially

described? $(3$ points$)$

e$)$ Ms$.$ Magnan sets herself a goal of amassing $$1$ million in her retirement account by the

time she retires. In addition to PLP$$s annual contributions, Ms$.$ Magnan contributes to the

account $$500$ every month over the $12-$year accumulation period $($starting one month

from now$).$ Also, she expects to receive a $$15,000$ bonus $4$ years from now which she

will also put into her retirement account. Will Ms$.$ Magnan be able to achieve