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How to Amortize a Loan


Amortization:  Literally to "kill off" (root: mort) the outstanding balance of a loan by making equal payments on a regular schedule (usually monthly). The payments are structured so that the borrower pays both interest and principal with each equal payment.

A payments and amortization calculator is available (no charge, no registration) to help you make quick calculations. But for those who really want to undertand the ins and outs of mortgage amortization, the following will explain everything as a mathematical formula.

To begin, here are the definitions of each of the variables used in the formula.

P = principal, the initial amount of the loan
I = the annual interest rate (from 1 to 100 percent)
L = length, the length (in years) of the loan, or at least the length over which the loan is amortized.
J = monthly interest in decimal form = I / (12 x 100)
N = number of months over which loan is amortized = L x 12

The following assumes a typical conventional loan where the interest is compounded monthly. Okay now for the big monthly payment (M) formula, it is:

M = P x _____________
              1 - ( 1 + J ) ^ -N
So to calculate it, you would first calculate 1 + J then take that to the -N (minus N) power, subtract that from the number 1. Now take the inverse of that (if you have a 1/X button on your calculator push that). Then multiply the result times J and then times P.

The formula above allows you to calculate the monthly payment, M. To calculate the amortization table you need to do some iteration.

Step 1: Calculate H = P x J, this is your current monthly interest
Step 2: Calculate C = M - H, this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for that month
Step 3: Calculate Q = P - C, this is the new balance of your principal of your loan.
Step 4: Set P equal to Q and go back to Step 1: You thusly around until the value Q (and hence P) goes to zero.
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