$5$

$24$ points

Direction: Make sure you show all the steps on paper. You can upload it as an image file on Canvas or email it to me$.$ If you email it to me$,$ make sure the time of your Exam submission match the time of your email.

Question:

Maria, a $25-$year$-$old teacher, wants to start saving for her retirement. Maria wants a comfortable retirement, so she needs to have one million dollars in her saving account, which pays $4\mathrm{.}8\%$ annual interest rate, when she reaches $65$ years of age.

A$.$ How much should Maria deposit into her saving account monthly now? Round your answer to the nearest cent. $(8$ pts$)$

B$.$ If Maria wants the one million dollars in her saving account to last $20$ years into her retirement, how much could she withdraw from the saving account monthly for retirement? You can assume the saving account will pay the same $4\mathrm{.}8\%$ annual interest rate. Round your answer to the nearest cent. $(8$ pts$)$

C$.$ If Maria increases her monthly deposit in part $($A$)$ by $$400,$ how much will be in her saving account if she wants to retire at $60$ years of age? Round your answer to the nearest cent. $(8$ pts$)$

Useful Formula: Mathematics of Finance

$S=$ the future value, $R=$ the periodic payment, $i=$ the interest rate per period, $n=$ the number of periods

$S=R(\frac{1-(1+i{)}^n}{1-(1+i)})=R(\frac{(1+i{)}^n-1}{i})$

$P=S(1+i{)}^{-n}=R(\frac{1(1+i{)}^{-n}}{i})$

$R=\frac{iP}{1-(1+i{)}^{-n}}=\frac{iS}{(1+i{)}^n-1}$