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# Mortgage calculator

# Mortgage calculator

# Mortgage calculator

Our estimated monthly payment provides an overview of everything that makes up your payment: such as principal and interest, plus additional costs — like taxes and insurance. The more info you’re able to provide, the more accurate your total monthly payment estimate will be.

If you’re really into math and want to know how the numbers work, here’s how to calculate your monthly mortgage payments on a fixed-rate loan:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Let’s break that down a little further. The variables are as follows:

- M = monthly mortgage payment
- P = the principal, or the initial amount you borrowed.
- i = your monthly interest rate. Your lender likely lists interest rates as an annual figure, so you’ll need to divide by 12, for each month of the year. So, if your rate is 5%, then the monthly rate will look like this: 0.05/12 = 0.004167.
- n = the number of payments over the life of the loan. If you take out a 30-year fixed rate mortgage, this means: n = 30 years x 12 months per year, or 360 payments.

As mentioned above, the longer the loan, the less you’ll pay each month. You will, however, also pay more in total because interest compounds. Essentially, you’ll pay interest on interest. So you multiply the interest rate by itself for each term of payment — hence the exponent in the formula. That will have a great bearing on your decision between a 30-year fixed-rate and a 15-year.

Say you’ve decided to buy a home that’s appraised at $500,000, so you take out a $400,000 loan with an interest rate of 3.5%. First, let’s take a look at a 30-year loan. For quick reference, again, the formula is:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Our P, or principal, is $400,000.

Remember, with i, we must take the annual interest rate given to us — 3.5%, or 0.035 — and divide by 12, the number of months in a year. This calculation leaves us with 0.002917, or i.

Our n, again, is the number of payments. And with one payment every month for 30 years, we multiply 30 by 12 to find n = 360.

When all s said and done, for a 30-year loan at 3.5% interest, we’ll pay $1,796.18 each month.

For a 15-year loan, the math is nearly identical. All that’s different is the value of n. Our loan is half the length, and so the value for n is 180. Each month we’ll pay $2,859.53, over 60% more than with the 30-year loan.

Over the length of the loan, though, the 15-year loan is a far better deal, considering the interest you pay — $514,715 in total. With the 30-year, you pay $646,624 total — over $100,000 more.

Your decision between these two, quite simply, hinges on whether or not you can float the significantly higher monthly payments for a 15-year loan.

A little math can go a long way in providing a “ how much house can I afford? ” reality check.

NerdWallet’s Mortgage Calculator makes it easy to compare common loan types to see how each type of loan affects your monthly payment. We source the latest weekly national average interest rate from Freddie Mac, so you can accurately estimate and compare your monthly payment for a 30-year fixed. 15-year fixed. and 5/1 ARM.

To help pick the right mortgage for you, you should consider the following:

- How long do you plan to stay in your home?
- How much financial risk can you accept?
- How much money do you need?

15- or 30-year fixed rate loan: If you’re settled in your career, have a growing family and are ready to set down some roots, this might be your best bet because the interest rate on a fixed-rate loan never changes.

In general, for a 30-year fixed loan, you will have the lowest monthly payment but the highest interest rate. However, with a 15-year fixed, you’ll have a higher payment, but will pay less interest and build equity and pay off the loan faster.

It’s worth noting though, that if other fees are rolled into your monthly mortgage payment, such as annual property taxes or homeowner’s association dues, there may be some fluctuation over time.

5/1 ARM and adjustable-rate mortgages: These most often appeal to younger, more mobile buyers who plan to stay in their homes for just a few years or refinance when the teaser rate is about to end.

These loans have interest rates that reset at specific intervals. They typically begin with lower interest rates than fixed-rate loans, sometimes called teaser rates. After the initial term ends, the interest rate — and your monthly payment — increases or decreases annually based on an index, plus a margin.

Paying a lower interest rate in those initial years could save hundreds of dollars each month that could fund other investments. But be careful. Your interest rate and monthly payment will increase after the introductory period, which can be 3, 5, 7 or even 10 years, and can climb substantially depending on the terms of your specific loan.