$($Solving a comprehensive$$ problem$)$ You would like to have

$$$$57$ comma $00057,000$

in

$1515$

years. To accumulate this$$ amount, you plan to deposit an equal sum in the bank each year that will earn

$66$

percent interest compounded annually. Your first payment will be made at the end of the year.

a$.$ How much must you deposit annually to accumulate this$$ amount?

b$.$ If you decide to make a large$$ lump$-$sum deposit today instead of the annual$$ deposits, how large should this$$ lump$-$sum deposit$$ be$?($Assume you can earn

$66$

percent on this$$ deposit.$)$

c$.$ At the end of $5$ years, you will receive

$$$$10$ comma $00010,000$

and deposit this in the bank toward your goal of

$$$$57$ comma $00057,000$

at the end of year

$1515.$

In addition to the$$ lump$-$sum deposit, how much must you deposit in equal annual$$ amounts, beginning in year$1,$ to reach your$$ goal? $($Again$,$ assume you can earn

$66$

percent on your$$ deposits.$)$

Question content area bottom

Part $1$

a$.$ How much must you deposit annually to accumulate this$$ amount?

$$$$2,448\mathrm{.}882,448\mathrm{.}88$

$($Round to the nearest$$ cent.$)$

Part $2$

b$.$ If you decide to make a large$$ lump$-$sum deposit today instead of the annual$$ deposits, how large should the$$ lump$-$sum deposit$$ be$?$

$$$$23,784\mathrm{.}1123,784\mathrm{.}11$

$($Round to the nearest$$ cent.$)$

Part $3$

c$.$ If you deposit

$$$$10$ comma $00010,000$

received at the end of $5$ years in the$$ bank, what will the amount grow to by the end of year

$1515?$

$$$$17,908\mathrm{.}4817,908\mathrm{.}48$

$($Round to the nearest$$ cent.$)$

Part $4$

In addition to the$$ lump$-$sum deposit, how much must you deposit in equal annual$$ amounts, beginning in year$1,$ to reach your$$ goal?