# How to Calculate Your Mortgage Payments

By
Mortgage and Lending with Empire Loans

Calculating your mortgage payment involves some relatively tricky math to end up with some relatively neat equations. From basic principles you need to targe a stream of monthly payments that when present valued will equal the mortgage principle amount taken out today.

If you are planning on setting up a spreadsheet to calculate mortgage payments see our 'mortgage amortization schedule' which will show you more spreadsheet calculations you can use.

The following is a step by step guide that will show you how mortgage lending companies calculate your mortgage payment. First, we need some definitions:
PF = payment frequency, the number of payments per year. Use 12 for monthly.
I = interest rate
i = effective interest rate (we're going to calculate this)
n = period (the number of payments - the term or number of years in the mortgage times the number of payments per year.)

For the first step, calculate i. You can think of this as the effective interest rate per month:
i = (1 + I/PF)^(12/PF) - 1

Next, calculate n (this is the number of payments in your mortgage):
n= PF X term of mortgage

Now we need to calculate an annuity factor.
Annuity factor = {1 - [1/(1+i)]^n}/i

And finally,
Payment = Principal/Annuity factor

Lets do a quick example:
\$100,000 mortgage at 7% interest. We'll assume a 30 year mortgage, with monthly payments.
i = (1+.07/12)^(12/12) - 1
= (1+1.00583333333)^1 - 1
= 1.00583333333 - 1
= .0058333333
Next, calculate n:
n= 12 X 30 (12 monthly payments, times 30 years)
= 360

Annuity factor
= {1 - (1/(1+i))^360}/.00583333333
= {1 - (1/1.0058333333)^360}/.0058333333
= {1-.994200497^360}/.0058333333
= {1-.123205853}/.005833333
= .876794147/.0058333333
= 150.3075

Payment = 100000/150.3075
= \$665.30

Therefore your monthly mortgage payment would be \$665.30. You can repeat this calculation for any interest rate, term, or mortgage amount.

There are certainly numerous online calculators including our Online Mortgage Calculator. If you prefer to calculate offline, use of a spreadsheet is warranted. You should be able to duplicate the above calculations, Simply set up cells that act as inputs for the interest rate, term of the mortgage, and the mortgage principle and the above calculations will allow you to calculate payments quickly.