You are trying to decide how much to save for retirement. Assume you plan to

save $$4000$ per year with the first investment made one year from now. You think

you can earn $5\%$ per year on your investments and you plan to retire in $43$ years,

immediately after making you last $$4000$ investment.

a$.$ How much will you have in your retirement account on the day you retire?

b$.$ If$,$ instead of investing $$4000$ per year, you wanted to make one lump$-$sum

investment today for your retirement that will result in the same etirement saving,

how much would that lump sum need to be$?$

c$.$ If you hope to live for $20$ years in retirement, how much can you withdraw every

year in retirement $($starting one year after retirement$)$ so that you will just exhaust

your savings with the $20$ th withdrawal $($assume your savings will continue to earn

$5\%$ in retirement$)?$

d$.$ If$,$ instead, you decide to withdraw $$300,000$ per year in retirement $($again with

the first withdrawal one year after retiring$),$ how many years will it take until you

exhaust your savings? $($Use trial$-$and$-$error, a financial calculator: solve for $"N",$ or

Excel: function NPER$)$

e$.$ Assuming the most you can afford to save is $$1000$ per year, but you want to

retire with $$1$ million in your investment account, how high of a return do you

need to earn on your investments? $($Use trial$-$and$-$error, a financial calculator: solve

for the interest rate, or Excel: function RATE$)$

Inputs:

Annual Savings

Investment Return

Retirement in

Retirement Horizon

a$.$ Account Value

h$.$ Todays Lump Sum

c$.$ Retirement Annual

Withdrawal

d$.$ Years of retirement

e$.$ Rate required