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: