How Do I Calculate My Monthly Mortgage Payment?

The math behind the mortgage payment calculater

Overview

Put simply, a mortgage is a loan intended to help a borrower purchase a home. The interest rate is the ROI for the lender, and is used in calculating the monthly payment made to the lender. For a lender to guarantee to make their money back they use the home and land as collateral incase there is a default.

The following formula will be used to calculate the fixed payment of your loan:

M = L [i (1+i)^n] / [(1+i)^n-1]

The equation variables are as follows:

Variable Value
M This is the monthly mortgage payment. The answer.
L The loan amount your borrowing, or the principal.
i Your monthly interest rate. The interest rate you will get from the broker is the yearly interest rate. To calculate the monthly rate you will need to divide the interest rate by 12 (months). So a 4.125% interest rate will be i = 4.125%/12 = 0.0034375.
n This is the number of monthly payments you will be making. If you take a 30-year loan then you will have 30*12 = 360 months/payments.

The main components of a loan that you should be aware of are Principal, Interest, Taxes, and Insurance. PITI are major factors when it comes to calculating the loan. Insurance on loans PMI are usually added when the down payment is less than 20%, this insurance protects the lender in case the borrower cannot pay back the loan. The insurance also allows the lender to sell the loan to investors who will be assured their debt investment will be paid back to them.

While PITI makes up a usual mortgage, some mortgage monthly payments do not include taxes and insurance, making the monthly payment lower, however, the borrower has to pay the taxes and insurance on their own.

Mortgage Payment Example

In our example we will assume we are buying a home valued at $500,000. We will be taking a 30-year-fixed rate mortgage of 4.125% interest rate with a loan amount of $375,000 making our down payment 25%. The amortization schedule will consist of 360 payments.

We will be calculating for M (Monthly mortgage payment):

Variable Value
L $375,000.00
i 4.125%/12 = 0.0034375
n 30*12 = 360

The best approach for doing this without an online calculator (since your learning the math behind your loan payment) would be to setup an EXCEL sheet. This will allow you to easily make changes to the rate, loan amount, and duration, to automatically calculate the changes for you. You can setup the numbers and calculations in different cells, depending on your level of experience working with excel.

The following walkthrough shows you a basic approach that you can quickly setup.

Excel mortgage calculator walk through

*For the less savvy excel user: B2, B3 etc. is the location of the cell with the specified data set. When you type the = sign you can simply hover over and select the cell you want with your mouse. E.g. B2 = $375,000.00

The Amortization Table

A more complex approach, which we will not be going into detail here, is calculating the amortization table. The amortization table shows the breakdown of all 360 payments, with details on how the balances between the principle and interest payments are divided. Basically, at the beginning of your payment period, a bigger percentage of your loan payment will be towards interest and less towards your principle, further down the years your monthly payment will reverse, making a bigger percentage of your monthly payment towards principle.

The following is an example of what the amortization table looks like. Showing you the first 10 years and the last 10 years of your loan payments. The numbers highlighted in red show how the monthly payment principle and interest will reverse.

Amortitization table example

*The above table is a screenshot of khanacadamys mortgage calculator that you can download from their website.

Finally, the math for some mortgages can be much more complex than this simple example. There are many free mortgage calculators you can download or use online that allow you to calculate taxes, insurance and show you the full amortization rate. However, now you know the math behind your mortgage payment.