Mortgage Payment Calculator

Instructions: Compute the required monthly mortgage payment, by indicating the total loan amount, the nominal annual interest rate (\(r\)), and the number of years to repay the loan (\(n\)). You will be shown step-by-steps calculations as well as a full amortization schedule:

Loan Amount =
Annual Interest Rate \((r)\) =
Number of years \((n)\) =

Mortgage Payment Calculator

More about the this monthly mortgage payment calculator so you can better understand how to use this solver. A monthly payment is the amount a borrower needs to make on a monthly basis in order to pay back for a loan.

In math terms, the monthly mortgage payment is the amount that needs to be made every month in order to repay loan of $\(\L\), with an agreed upon interest rate of \(r\), and term of the loan in \(n\) years.

Mortgage Payment Formula

The monthly mortgage payment is computed using the following mortgage formula:

\[ P = \displaystyle \frac{\frac{r}{12} L \left(1 + \frac{r}{12} \right)^{N} }{ \left(1 + \frac{r}{12} \right)^{N} -1 } \]

The above formula may seem complicated, but it truly isn't. If you have ever gone through the processes of talking to a mortgage lender, you have probably seen them using some basic calculator, using maybe values from a table.

And believe it or not, that is exactly the same as what you get using the above mortgage formula. Those mortgage lender agents will find those "factors" based on the interest rate and term of the loan. Then, they get the factor and divide the loan amount. And, magically, you get the monthly payment amount.

Mortgage Payment Calculator

Mortgage Amortization Schedule

What is an amortization schedule? That is a commonly asked question: An amortization schedule is a table that shows the monthly payment along with a breakdown of how much of that payments goes to the principal, and how much goes to pay interest, as well as the balance of the loan for all months in the life of the loan.

Out of what you pay off each month, a certain amount goes to pay interest, which is based on how much is currently owed. As you go paying the principal off, your amount owed goes decreasing and so does the interest due.

Notice that the mortgage payments are typically fixed (assuming fixed interest rate), which means that as you go paying your mortgage off, more of what you pay monthly goes to reduce your principal, and the amortization table shows you precisely that, for each month in the future until the completion of the payments of the loan.

Where Do I get the Amortization Schedule

Most loan calculators will give you an amortization table of some sort, but that is not always the case. Our mortgage calculator will show you the mortgage payment formula, the monthly payment obtained using the formula, and right below that it will show you a complete amortization table.

Notice this table can be pretty long. Indeed, for a 30 year loan, you will have 30 x 12 = 360 months, so the amortization table will have 360 rows.

Mortgage Calculator

Relationship between Mortgage payment and Present Value

The mortgage payment, or more specifically, the amount paid monthly for a mortgage payment is tightly related to the idea of present value calculation.

Indeed, the monthly mortgage payment is such that the sum of the present value of all the monthly payments equals the amount borrowed.

Put it simply, if you take each of the monthly mortgage payments you make (for example, if your loan is a 30-year one, you will have 360 of those monthly payments), and you discounted them by the corresponding monthly discount rate (which is obtained dividing the nominal annual rate by 12) and bring each of them to present value and added them, what you get is the total amount you are borrowing. Nice, isn't.

That is why it is said that the annual interest rate that you are quoted at your mortgage company is a nominal rate, because the discounting is done at the monthly level. You can use our effective rate calculator to see the precise rate you are paying given a quote rate.

Relationship between Interest Rate and Mortgage payments

One of the main factors determining how much you will pay monthly for your mortgage loan is the interest rate. There is the obvious fact that the higher the interest rate is, the higher your mortgage payment will be, but there is a lot more to that .

The relationship is not really linear between mortgage rate and mortgage payment, and indeed, a small increase in the interest rate can bring a relatively large increase in total fees throughout the life of the loan.

Another important element is the term of the loan. Longer term loans will make you pay more monthly. There are some interesting mathematical exercises you can conduct when dealing with mortgages.

One interesting one is what happens when you instead of paying your mortgage once a month, you pay it every 15 days (twice a month), but dividing the total monthly amount in 2, so you are paying the same amount each month, but you are "accelerating" the payment of the loan. This simple action may substantially reduce the total amount in interest paid.

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