Amortization Schedule Calculation

NOTE: This describes how to calculate the amortization schedule for United States mortgages.

First you must define some variables to make it easier to set up:

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.

The following assumes a typical conventional loan where the interest is compounded monthly. First I will define two more variables to make the calculations easier:

J = monthly interest in decimal form = I / (12 x 100)

N = number of months over which loan is amortized = L x 12

Okay now for the big monthly payment (M) formula, it is:

                              J
         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. Sorry, for the long way of explaining it, but I just wanted to be clear for everybody.

The one-liner for a program would be (adjust for your favorite language):

         M = P * ( J / (1 - (1 + J) ** -N))

So now you should be able to calculate the monthly payment, M. To calculate the amortization table you need to do some iteration (i.e. a simple loop). I will tell you the simple steps :

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 loop around until the value Q (and hence P) goes to zero.