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You are trying to decide how much to save for retirement. Assume you plan to save $$6,500$ per year with the first investment

made one year from now. You think you can earn $10\%$ per year on your investments and you plan to retire in $34$ years,

immediately after making your last $$6,500$ investment.

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

b$.$ If$,$ instead of investing $$6,500$ per year, you wanted to make one lump$-$sum investment today for your retirement that will

result in the same retirement saving, how much would that lump sum need to be$?$

c$.$ If you hope to live for $16$ 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 $16$ th withdrawal $($assume your savings will continue to earn

$10\%$ in retirement$)$

d$.$ If$,$ instead, you decide to withdraw $$200,000$ per year in retirement $($again with the first withdrawal one year after retiring$),$

how many years will it take until you exhaust your savings?

e$.$ Assuming the most you can afford to save is $$1,300$ per year, but you want to retire with $$1,000,000\mathrm{.}00$ in your

investment account, how high of a return do you need to earn on your investments?

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

The amount in the retirement account in $34$ years would be $$1,595,598\mathrm{.}54.($Round to the nearest cent.$)$

b$.$ If$,$ instead of investing $$6,500$ per year, you wanted to make one lump$-$sum investment today for your retirement that will

result in the same retirement saving, how much would that lump sum need to be$?$

You will need to make one lump sum investment today of $$62455\mathrm{.}74.($Round to the nearest cent.$)$

c$.$ If you hope to live for $16$ 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 $16$ th withdrawal $($assume your savings will continue to earn

$10\%$ in retirement$)?$

The amount you can withdraw every year in retirement is $$203944\mathrm{.}01.($Round to the nearest cent.$)$

d$.$ If$,$ instead, you decide to withdraw $$200,000$ per year in retirement $($again with the first withdrawal one year after retiring$),$

how many years will it take until you exhaust your savings?

You will exhaust your savings in years. $($Round to two decimal places.$)$