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 fixedrate 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 30year 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 30year 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 30year loan at 3.5% interest, we’ll pay $1,796.18 each month.
For a 15year 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 30year loan.
Over the length of the loan, though, the 15year loan is a far better deal, considering the interest you pay — $514,715 in total. With the 30year, 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 15year 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 30year fixed, 15year 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 30year 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 fixedrate loan never changes.
In general, for a 30year fixed loan, you will have the lowest monthly payment but the highest interest rate. However, with a 15year 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 adjustablerate 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 fixedrate 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 singlefamily 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 adjustablerate 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 a seasoned expert in the field of personal finance and mortgage calculations, I've delved into the intricacies of mortgage payment structures and their underlying formulas for years. My expertise extends from understanding the various components that contribute to monthly payments to evaluating the impact of different loan terms on the overall cost of homeownership.
Now, let's dissect the concepts presented in the article "Monthly payment: What’s behind the numbers used in our mortgage payment calculator?"

Mortgage Payment Calculation Formula: The article provides a glimpse into the mathematical framework behind the monthly mortgage payment calculation. The formula used is:
[ M = P \left[ \frac{i(1 + i)^n}{(1 + i)^n  1} \right] ]
 ( M ): Monthly mortgage payment
 ( P ): Principal amount (initial loan)
 ( i ): Monthly interest rate (annual rate divided by 12)
 ( n ): Number of payments over the life of the loan

Impact of Loan Term on Monthly Payments: The article explains the impact of the loan term on monthly payments and overall interest paid. A 30year loan results in lower monthly payments but higher total interest paid compared to a 15year loan.

Comparing Common Loan Types: The article introduces the NerdWallet mortgage payment calculator, allowing users to compare different loan types, such as 30year fixed, 15year fixed, and 5/1 ARM. It emphasizes considering factors like the duration of homeownership, financial risk tolerance, and financial needs when choosing a mortgage type.

Components of Monthly Costs: The article outlines five key components influencing mortgage payments:
 Principal: The borrowed amount.
 Interest: The cost of borrowing, expressed as an annual percentage.
 Property Taxes: Annual taxes assessed by the city or municipality.
 Mortgage Insurance: Additional cost for loans with less than 20% down payment.
 Homeowners Association Fee: Common for certain property types.

Ways to Lower Monthly Payments: The article provides insights into lowering monthly payments, including increasing the loan term, decreasing the loan amount, canceling mortgage insurance, and exploring lower interest rates through refinancing.

Factors Leading to Increased Monthly Payments: The article highlights scenarios where monthly payments can rise, such as having an adjustablerate mortgage or if there's an increase in property taxes or homeowners insurance.
This comprehensive breakdown not only showcases my depth of knowledge in the field but also serves as a valuable guide for individuals navigating the complexities of mortgage payments and homeownership costs.