(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 > 0 be the interest rate charged (per period), R the size of the per period payment (paid at the end of each period), and Pt the amount that is still owed after t periods. So P0 = P

Personal Finance
13th Edition
ISBN:9781337669214
Author:GARMAN
Publisher:GARMAN
Chapter9: Obtaining Affordable Housing
Section9.4: Financing A Home
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(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 > 0 be the interest rate charged (per period), R the size of the per period payment (paid at the end of each period), and Pt the amount that is still owed after t periods. So P0 = P
(a) Find P1.
(b) Find a first order linear recurrence for Pt.
(c) Show that the solution to your recurrence relation is
Pt = (P-(R/i))(1+i)^t + (R/i)

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