Adam just graduated from college with a $$35,000$ student loan to pay off. The loan charges $6\%$ interest compounded monthly $($so the interest charged per month is $6\frac{\%}{12}=0\mathrm{.}5\%,$ based on the remaining balance$).$ He makes payments of $$400$ per month.

a$.$ Let $A_n$ be the remaining balance of the loan at month $n.$ Assume that $A_0=35,000.$ Give a formula for $A_n$ in terms of $A_{n-1}.$

b$.$ Use Excel $($or Matlab or other technology tool$)$ to help determine how long it will take to pay this loan off.

c$.$ What were the total amount of payments made towards the loan? $($This is the monthly payment multiplied by the number of payments.$)$

d$.$ What was the total amount of interest paid during the period of the loan? $($Interest is the difference between the amount paid and the amount of the loan.$)$

e$.$ If the payments were instead $$800$ per month, then how long would it take to pay off? What would be the total amount of interest paid?

Submit your spreadsheet $($or Matlab script$)$ used for # to Moodle.