Today is January $1,2027$ and it is your $40$th birthday. You are in great health and are leading a happy life, but you are

thinking that you would like to better understand your retirement savings. With renewed commitment, you sit down

to evaluate your situation.

You have saved $$60,000$ thus far in your Roth IRA plan, which is your sole means of retirement savings $($since this is a

Roth IRA, we will ignore taxes throughout your evaluation$).$ You expect to work until the age of $65$ and you expect to

make annual deposits of $$6,000,$ the current maximum allowed for a Roth IRA, beginning next year through age $65.$

You expect to make your first annual withdrawal at age $66$ and your final withdrawal at age $85.$ If you are going to

meet your goal of maintaining your current lifestyle in retirement, you know you need to inflation$-$adjust your

expected annual withdrawals needed for $100\%$ total income replacement. Your current annual income is $$70,000$

and you expect the annual rate of inflation over your entire planning period to average $2\%($i$.$e$.,$ the FEDs target

inflation rate$).$ Based on your portfolio selection consisting mainly of an S&P $500$ Index Fund, you expect to earn an

$8\mathrm{.}5\%$ average annual rate of return.

After "crunching the numbers", you come to the stark realization that your current savings plan does not adequately

cover your estimated withdrawal needs. You indulge in a piece of birthday cake and begin to address the following

issues:

$1\mathrm{.}1$ At age $65,$ how much will your estimated shortfall in retirement savings be$?(10$ points$)$

$1\mathrm{.}2$ By how much do you need to increase your total annual Roth IRA contribution to have adequate savings for your

estimated withdrawal needs? $(10$ points$)$

$1\mathrm{.}3$ As an alternative to your estimate in $1\mathrm{.}2,$ perhaps you can invest more aggressively to achieve a higher expected

return. If you maintain your total annual Roth IRA deposits at $$6,000,$ what average annual rate of return will

you need to earn to adequately cover your estimated withdrawal needs? $(10$ points$)$

$1\mathrm{.}4$ As your daughter wraps her arms around you in a glorious birthday hug, you realize you would also like to build

a $$legacy of giving$$ into your savings. You wish to provide $$25,000$ annually to your heirs beginning at age $86$

and continuing in perpetuity. If you make annual deposits in the same portfolio as your retirement savings

beginning next year through your $85$th birthday to cover this obligation, what must those annual deposits be$?$

Assume no inflation effects on the withdrawal amounts and that your average annual rate of return is the same

as you are earning on your retirement savings. $(5$ points$)$

$1\mathrm{.}5$ Revisit $1\mathrm{.}4$ above and assume that while the first withdrawal will be $$25,000,$ allow all subsequent withdrawals

to grow by the estimated annual inflation rate. If you make annual deposits into a mutual fund beginning next

year through your $85$th birthday to cover this obligation, what must those annual deposits be$?$ Assume that your

average annual rate of return is the same as you are earning on your retirement savings. $(5$ points$)$

$1\mathrm{.}6$ You would now like to consider the effect inflation has on your future retirement savings. You decide to conduct

a sensitivity analysis $($i$.$e$.,$ What$-$if$-$Analysis$)$ to consider how sensitive your projected shortfall from question $1\mathrm{.}1,$

Payment Needed is from question $1\mathrm{.}2,$ and how much more dollars you must invest per year from question $1\mathrm{.}2$ is

to the expected annual inflation rate. Consider a range of inflation rates from $1\%-10\%$ in your analysis to see

the impact inflation has on your retirement savings and why $$sticky$$ high$-$inflation is so damaging to

investments. $(10$ points$)$