You would like to have $$$$72000$ in $12$ years. To accumulate this$$ amount, you plan to deposit an equal sum in the bank each year that will earn $9\%$ 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 the$$ lump$-$sum deposit$$ be$?($Assume you can earn $9\%$ on this$$ deposit.$)$

c$.$At the end of year$5,$ you will receive $$$$20000$ and deposit it in the bank in an effort to reach your goal of $$$$72000$ at the end of year $12.$ In addition to the$$ lump$-$sum deposit, how much must you invest in $12$ equal annual deposits to reach your$$ goal? $($Again$,$ assume you can earn $9\%$ on this$$ deposit.$)$