. (Note, this is how mortgage payments are calculated.) Payments on a loan are amortized when a fixed amount is paid at the end of each time period in order to pay off both the principle of the loan and the interest accumulated up to that point. At the end of each period, interest is charged on the amount still owing. Let P be the initial amount of the loan, and i>o be the interest rate charged (per period), R the size of the per period payment (paid at the end of each period), and P, the amount that is still owed after t periods. So Po =P (a) Find Pi. (b) Find a first order linear recurrence for P. (c) Show that the solution to your recurrence relation is R (i)' P. - (P-4) 1+ 9 + 4 . (Note, this is how mortgage payments are calculated.) Payments on a loan are amortized when a fixed amount is paid at the end of each time period in order to pay off both the principle of the loan and the interest accumulated up to that point. At the end of each period, interest is charged on the amount still owing. Let P be the initial amount of the loan, and i>o be the interest rate charged (per period), R the size of the per period payment (paid at the end of each period), and P, the amount that is still owed after t periods. So Po =P (a) Find Pi. (b) Find a first order linear recurrence for P. (c) Show that the solution to your recurrence relation is R (i)' P. - (P-4) 1+ 9 + 4