## Monthly payment: What’s behind the numbers used in our mortgage payment calculator?

The NerdWallet mortgage payment calculator cooks in all the costs that are wrapped into your monthly payment, including principal and interest, taxes and insurance. You’ll just need to plug in the numbers. The more info you’re able to provide, the more accurate your total monthly payment estimate will be.

For example, you may have homeowners association dues built into your monthly payment. Or mortgage insurance, if you put down less than 20%. And then there’s property taxes and homeowners insurance. It helps to gather all of these additional expenses that are included in your monthly payment, because they can really add up. If you don’t consider them all, you may budget for one payment, only to find out that it’s much larger than you expected.

For you home gamers, here’s how we calculate your monthly mortgage payments on a fixed-rate loan:

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

The variables are:

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.

## Interest: The difference 15 years can make

The longer the term of your loan — say 30 years instead of 15 — the lower your monthly payment but the more interest you’ll pay.

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.

## Comparing common loan types

NerdWallet’s mortgage payment 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 Zillow, so you can accurately estimate and compare your monthly payment for a 30-year fixed, 15-year fixed, and 5/1 ARM.

To pick the right mortgage, 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.

If other fees are rolled into your monthly mortgage payment, such as annual property taxes or homeowners 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 three, five, seven or even 10 years, and can climb substantially depending on the terms of your loan.

## What are my monthly costs for owning a home?

There are five key components in play when you calculate mortgage payments

Principal: The amount of money you borrowed for a loan. If you borrow $200,000 for a loan, your principal is $200,000.

Interest: The cost of borrowing money from a lender. Interest rates are expressed as a yearly percentage. Your loan payment is primarily interest in the early years of your mortgage.

Property taxes: The yearly tax assessed by the city or municipality on a home that is paid by the owner. Property taxes are considered part of the cost of owning a home and should be factored in when calculating monthly mortgage payments. However, lenders don’t control this cost and so it shouldn’t be a major factor when choosing a lender.

Mortgage insurance: An additional cost of taking out a mortgage, if your down payment is less than 20% of the home purchase price. This protects the lender in case a borrower defaults on a mortgage. Once the equity in your property increases to 20%, you can stop paying mortgage insurance, unless you have an FHA loan.

Homeowners association fee: This cost is common for condo owners and some single-family neighborhoods. It’s money that must be paid by owners to an organization that assists with upkeep, property improvements and shared amenities.

In addition to the monthly costs addressed in our mortgage payment calculator, keep in mind that there are other upfront costs in addition to your down payment. These costs include property and loan related fees, insurance and title fees. Find out more about mortgage closing costs

## Can I lower my monthly payment?

There are a few ways to lower your monthly payment. Our mortgage payment calculator can help you understand if one of them will work for you:

Increase the term of the loan. The longer you take to pay off the loan, the smaller each monthly mortgage payment will be. The downside is that you’ll pay more interest over the life of the loan.

Decrease the size of the loan. If you have a smaller loan balance to begin with, you’ll need to fork over less each month to pay it off.

Get to the point where you can cancel your mortgage insurance. Many lenders require you to carry mortgage insurance (which protects the lender in case you default on the loan) if you put less than 20% down. This is another charge that gets added to your monthly mortgage payment. You can usually cancel mortgage insurance when your remaining balance is less than 80% of your home’s value. However, FHA loans can require mortgage insurance for the life of a loan.

Look for a lower interest rate. You can think about refinancing (if you already have a loan) or shop around for other loan offers to make sure you’re getting the lowest interest rate possible.

## Can my monthly payment go up?

Your monthly payment can rise in a few cases:

You have an adjustable-rate mortgage in which your payment stays the same for an initial term (such as five, seven or 10 years) and then readjusts annually.

If you have an escrow account to pay for property taxes or homeowners insurance, because those taxes or insurance premiums may increase. Your monthly mortgage payment includes the amount paid into escrow, so the taxes and premiums affect the amount you pay each month.

You may have been assessed fees. Check your mortgage statement or call your lender.

» MORE FOR CANADIAN READERS: Canada mortgage payment calculator

As an expert in personal finance and mortgage calculations, let me delve into the intricacies of the article discussing the NerdWallet mortgage payment calculator and the various concepts associated with monthly payments, loan types, and factors influencing homeownership costs.

The article starts by emphasizing the importance of understanding all the costs wrapped into your monthly mortgage payment. The NerdWallet mortgage payment calculator is designed to include principal and interest, taxes, insurance, and other potential expenses like homeowners association dues or mortgage insurance for down payments below 20%.

The core mathematical formula used for calculating monthly mortgage payments on a fixed-rate loan is provided as: [ M = P \left[ \frac{i(1 + i)^n}{(1 + i)^n - 1} \right] ]

Here are the key variables explained:

- ( M ): Monthly mortgage payment
- ( P ): Principal amount (initial borrowed amount)
- ( i ): Monthly interest rate (annual interest rate divided by 12)
- ( n ): Number of payments over the life of the loan (loan term in years multiplied by 12)

The article then explores the impact of loan term on monthly payments and total interest paid, using a practical example with a $400,000 loan at 3.5% interest rate over 30 years versus 15 years.

Additionally, the article introduces the concept of comparing common loan types, such as 15-year fixed, 30-year fixed, and adjustable-rate mortgages (ARMs). It suggests considering factors like the duration of stay in the home, financial risk tolerance, and the amount of money needed.

The five key components affecting mortgage payments are outlined:

- Principal: The borrowed amount
- Interest: The cost of borrowing expressed as a yearly percentage
- Property taxes: Yearly tax assessed by the city or municipality
- Mortgage insurance: Additional cost if down payment is less than 20%
- Homeowners association fee: Common for condo owners and certain neighborhoods

The article also addresses ways to lower monthly payments, such as increasing the loan term, decreasing the loan size, canceling mortgage insurance, or securing a lower interest rate. Conversely, it warns about potential increases in monthly payments due to adjustable-rate mortgages or changes in property taxes or insurance premiums.

Overall, the article provides comprehensive insights into mortgage calculations, loan types, and factors influencing monthly payments and homeownership costs.