Required Lump$-$Sum Payment

To complete your last year in business school and then go through law school, you will need $$5,000$ per year for $4$ years, starting next year $($that is$,$ you will need to withdraw the first $$5,000$ one year from today$).$ Your uncle offers to put you through school, and he will deposit in a bank paying $9\%$ interest a sum of money that is sufficient to provide the $4$ payments of $$5,000$ each. His deposit will be made today. Do not round intermediate calculations. Round your answers to the nearest cent. If your answer is zero, enter $"0".$

a$.$ How large must the deposit be$?$

$ $$

b$.$ How much will be in the account immediately after you make the first withdrawal?

$ $$

How much will be in the account immediately after you make the last withdrawal?

$ $$