Your new bank account pays interest of $1\mathrm{.}5\%$ per year. You deposited $$10,000$ at the start of this year.

a$.$ At the end of every future year, you will withdraw the amount of interest that you earned during that year and spend it$.$ How much will be in the account at the end of five years $($after you withdrew and spent the interest earned during the fifth year$)?$

b$.$ Now assume instead that you will not make any withdrawals during the next five years. How much will be in the account at the end of five years?

c$.$ What are the present values of the final amounts calculated in parts a$.$ and b$.,$ if the appropriate discount rate is $3\%?$