Question:

Isabella, a $27-$year$-$old teacher, wants to start saving for her retirement. Isabella wants a comfortable retirement, so she needs to have one million dollars in her saving account, which pays $5\mathrm{.}8\%$ annual interest rate, when she reaches $67$ years of age.

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

B$.$ If Isabella 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 $5\mathrm{.}8\%$ annual interest rate. Round your answs to the nearest cent. $(8$ pts$)$

C$.$ If Isabella increases her monthly deposit in part $($A$)$ by $$500,$ how much will be in her saving account if she wants to retire at $62$ years of a 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

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

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

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