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Real Estate & Mortgage Calculators

Mortgage Calculations by Hand


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Determining the payment for a mortgage is a valuable tool in understanding the parts and basis of a mortgage. Using the formula displayed below, the payment for a mortgage can be calculated.

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 the length over which the loan is amortized).

The following assumes a typical conventional loan where the interest is compounded monthly. To make the calculations easier we need to define two more variables: 
J
= monthly interest in decimal form = I / (12 x 100) 
N
= number of months over which loan is amortized = L x 12

The monthly payment (M) formula is...

                              J
         M  =  P  x ------------------------
                 
                      1  - ( 1 + J ) ^ -N

To calculate the monthly payment, 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:

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

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.

The following is the formula 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:

  • q = amount of annual payment periods

  • r = interest rate

  • B = principle

  • m = payment amount

  • n = amount payment periods

  • LN = natural logarithm

 


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