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:

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

Programmers will see how this makes a trivial little loop to code, but I have found that many people now surfing on the Internet are NOT programmers and still want to calculate their mortgages! So this page was dedicated more to the latter.

Finding the Number of Periods given a Payment, Interest and Loan Amount

n = - (LN(1-(B/m)*(r/q)))/LN(1+(r/q))
# years = - 1/q * (LN(1-(B/m)*(r/q)))/LN(1+(r/q))

Where:

• q = amount of annual payment periods
• r = interest rate
• B = principal
• m = payment amount
• n = amount payment periods
• LN = natural logarithm

For Finding Remaining Principal Balance

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

• 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
• t=number of paid monthly loan payments

Canadian Formula

This was contributed to me by: Mike Morley (morleym@interlog.com)

Canadian mortgages are compounded semi-annually instead of monthly like
US
mortgages.
 
          Monthly Pmt =
(P*(((1+i/200)^(1/6)-1))/(1-(((1+i/200)^(1/6)))^-(n*12)))
 
          Where:
 
                        P = principal outstanding
                        i = annual interest rate percentage
                        n = number of years

Here is a easier to read representation:

                           i    1/6
                   ( 1 +  --- )       -   1
                          200
Pmt = Principal x  ------------------------
                                i   1/6    -12 x n
                   1 -  [ (1 + --- )     ] 
                               200

Or to convert canadian interest rates to US interest rates:

                           Can. Rate  1/6
US Rate =  1200 x [ ( 1 +  --------- )     - 1 ]
                              200

or as a formula, US Rate = 1200 * ((1 + Can.Rate/200)^(1/6) - 1)

You'll note if you plug this into the US formula you get the above formula for payment.