Susie just got hired at a new job that pays her $$5,000$ a month. She has student loan debt of $$10,000$ and her monthly expenses total $$800$ including rent. The student loan that she took out has an interest rate of $3\mathrm{.}25\%$ compounded monthly. $($Hint: This is not a steady state problem so be sure that you are accounting for any dependencies on time. Also, the compound interest every month is taken on the remaining balance of the loan.$)$

a$.$ How long will it take Susie to pay off her loans assuming she makes the maximum possible monthly payment?

b$.$ What is the net generation? Why?