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Mortgage Calculations
by Hand
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%) 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 we'll 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 Now for the big monthly payment (M) formula ... it is:
J
M = P x ------------------------
1 - ( 1 + J ) ^ -N
where 1 is the number one (it does not appear too clearly
on some browsers)
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 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). Here are 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 thusly loop around until the value Q (and hence P) goes to zero. Many people have asked how to find N (number of payments) given the payment, interest and loan amount. The answer to the actual formula is in the book: The Vest Pocket Real Estate Advisor by Martin Miles (Prentice Hall). Here's the formula:n = -1/q * (LN(1-(B/m)*(r/q)))/LN(1+(r/q)) Where:
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