Nina has just started saving for retirement. She wants to be able to withdraw $$6,700$ a month for $27$ years after retirement. $($The first withdrawal will come one month after she retires$).$ Nina has found the perfect retirement account that will provide her $1\mathrm{.}5\%$ interest compounded monthly.

A$.$ How much money should Nina have in her retirement account at retirement to be able to make these withdrawals of $$6,700$ a month all through her retirement?

B$.$ If Nina wants to make monthly deposits into her retirement account, starting next month and continuing for the next $12$ years until she retires, what should her monthly deposit be in order to have enough money at retirement?

NOTES:

Please provide your calculator inputs and output for each part $($A and B$).$ Even if you use the formulas instead of the calculator, please still provide the inputs$/$output $($just like you would on a calculator$)$ as follows: $N=,\frac{\text{I}}{Y}=($as $\%$ without $\%$ sign!$),PV=,PMT=,FV=$dots Remember, your $CY$ and $PY$ calculator values should be set to $1.$

Please enter ALL numbers as POSITIVE numbers even though you would need to enter a number as negative in your calculator!

Please use $4$ decimal places in all calculations throughout this problem. This will help to mitigate any potential concerns related to rounding in your answers.

Part A

$N=$

$\frac{\text{I}}{Y}=(as$ percent, $e.g.10\mathrm{.}25$ for $10\mathrm{.}25\%)$

$PV=$

$PMT=$

$FV=$

Part B

$N=$

$\frac{\text{I}}{Y}=(as$ percent, $e.g.10\mathrm{.}25$ for $10\mathrm{.}25\%)$

$PV=$

$PMT=$

$FV=$