$($Comprehensive problem$)$You would like to have $$$$52$ comma $000$ in $14$ years. To accumulate this$$ amount, you plan to deposit an equal sum in the bank each year that will earn $9$ 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 $9$ percent on this$$ deposit.$)$

c$.$At the end of five$$ years, you will receive $$$$10$ comma $000$ and deposit this in the bank toward your goal of $$$$52$ comma $000$ at the end of year $14.$ In addition to the$$ 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 $9$ percent on your$$ deposits.$)$

Question content area bottom

Part $1$

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

$$$

$$

enter your response here$($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$?$

$$$

$$

enter your response here$($Round to the nearest$$ cent.$)$

Part $3$

c$.$If you deposit $$$$10$ comma $000$ received at the end of five years in the$$ bank, what will the amount grow to by the end of year $14?$

$$$

$$

enter your response here$($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?

$$$

$$

enter your response here$($Round to the nearest$$ cent.$)$