# Mortgage Calculator: How to Calculate Your Monthly Payments

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There are quite a few factors that go into the calculation of your mortgage expenses, but most homebuyers like to begin by determining their monthly payments and the lifetime cost of the mortgage. Calculating these two figures is a good first step toward understanding all of your other expenses.

## How to Calculate Your Monthly Mortgage Payment

You can calculate your monthly mortgage payments using the following formula:

M = P [ I ( 1 + I )^N ] / [ ( 1 + I )^N – 1 ]

In order to find your monthly payment amount "M," you need to plug in the following three numbers from your loan:

• P = Principal amount (the total amount borrowed)
• I = Interest rate on the mortgage
• N = Number of periods (monthly mortgage payments)

A good way to remember the inputs for this formula is the acronym PIN, which you need to "unlock" your monthly payment amount. If you know your principal, interest rate and number of periods, you can calculate both the monthly mortgage payment and the total cost of the loan. Note that the formula only gives you the monthly costs of principal and interest, so you'll need to add other expenses like taxes and insurance afterward.

Also keep in mind that most lender quotes provide rates and term information in annual terms. Since the goal of this formula is to calculate the monthly payment amount, the interest rate "I" and the number of periods "N" must be converted into a monthly format. This means that you must convert your variables through the following steps:

1. Subtract your down payment amount from the home price to find the total borrowed "P"
2. Divide your quoted annual interest rate by 12 to get your monthly interest rate "I"
3. Multiply the number of years in your mortgage term by 12 to find the total number of monthly payments you will be making "N" – be careful not to confuse this with what the monthly payments will be, aka "M," which we will calculate later on

Once you've converted your inputs, you're ready to plug them into your formula. At this point, it becomes simple arithmetic. Make sure you have a calculator on hand to help with the calculations. To illustrate how this might look with numbers from a typical mortgage, we've provided the following example.

#### Example

Let's say you're trying to purchase a \$250,000 home by taking out a 30-year mortgage with a 20% down payment. The mortgage lender offers you an interest rate of 5% for this loan.

To calculate your total borrowed amount "P," first subtract your 20% down payment from the \$250,000 home price. This gives you a total borrowed amount of \$200,000.

P = \$250,000 – (20% of \$250,000) = \$250,000 - \$50,000 = \$200,000

Next, to calculate your monthly interest rate, divide your annual interest rate of 5% by 12 to obtain your monthly interest rate "I." Remember to convert your mortgage rate into decimals before dividing, so that you don't end up with a figure one hundred times higher than it should be.

I = 5% divided by 12 = 0.05/12 = 0.004167

Finally, obtain your total number of monthly payments "N" by multiplying the total number of years in your loan by 12. Since the loan in our example has a 30-year term, this comes out to 360 months.

N = 30 years X 12 months = 360

In our example, the three PIN variables come out to the following:

Variable
Value in this example
Principal "P"200,000
Interest rate "I"0.004167
Number of periods "N"360

Substituting them into the original equation to solve for monthly payment "M," we get:

M = P [ I ( 1 + I )^N ] / [ ( 1 + I )^N – 1 ]

M = 200,000 * [ 0.004167 ( 1 + 0.004167)^360 ] / [ ( 1 + 0.004167 )^360 – 1 ]

M = 200,000 * [ 0.004167 ( 1.004167 )^360 ] / [ ( 1.004167 )^360 – 1 ]

M = 200,000 * [ 0.004167 * 4.468278 ] / [ 4.468278 – 1 ]

M = 200,000 * 0.018618 / 3.468278

M = 200,000 * 0.005368

M = 1,073.64

Keep in mind that rounding may have a slight impact on your final answer for the monthly payment; your calculation may differ by a few dollars. As stated above, this formula doesn't account for any ongoing taxes or insurance premiums, and only accounts for your monthly mortgage payment. If you want to know the full estimate of your mortgage costs, you'll need to calculate the total cost of your mortgage loan, as shown below.

## How to Calculate the Total Cost of Your Mortgage

Once you have your monthly payment amount, calculating the total cost of your loan is easy. You will need the following inputs, all of which we used in the monthly payment calculation above:

• N = Number of periods (number of monthly mortgage payments)
• M = Monthly payment amount, calculated from last segment
• P = Principal amount (the total amount borrowed, minus any down payments)

To find the total amount of interest you'll pay during your mortgage, multiply your monthly payment amount by the total number of monthly payments you expect to make. This will give you the total amount of principal and interest that you'll pay over the life of the loan, designated as "C" below:

• C = N * M
• C = 360 payments * \$1,073.64
• C = \$368,510.40

You can expect to pay a total of \$368,510.40 over 30 years to pay off your whole mortgage, assuming you don't make any extra payments or sell before then. To calculate just the total interest paid, simply subtract your principal amount P from the total amount paid C.

• C – P = Total Interest Paid
• C – P = \$368,510.40 - \$200,000
• Total Interest Paid = \$168,510.40

At an interest rate of 5%, it would cost \$168,510.40 in interest to borrow \$200,000 for 30 years. As with our previous example, keep in mind that your actual answer might be slightly different depending on how you round the numbers.

## How to Account for Closing Costs

Once you've calculated the total principal and interest expense on your mortgage, factoring in closing costs or fees will be straightforward. Since closing costs are paid in full when you close on the loan, you can simply add them to your overall loan cost without using any long formulas. Some examples of upfront closing costs include the following:

• Mortgage lender fees
• Third-party mortgage fees
• Prepaid mortgage costs

While there may be other categories of upfront fees, the process for calculating them remains the same: Just add them to the total cost of the mortgage loan. Keep in mind that this will exclude any added monthly expenses paid in escrow, like taxes or homeowner's insurance. Our next section explains how to factor in monthly expenses.

## How to Account for Taxes and Recurring Expenses

Accounting for recurring charges like PMI and HOA fees requires a little more work, but even these aren't very difficult to calculate. You can find the total cost of recurring expenses by adding them together and multiplying them by the number of monthly payments (360 for a 30-year mortgage). This will give you the lifetime cost of monthly charges that exclude the cost of your loan.

The reverse is true for annual charges like taxes or insurance, which are usually charged in a lump sum, paid once per year. If you want to know how much these expenses cost per month, you can divide them by 12 and add the result to your mortgage payment. Most mortgage lenders use this method to determine your monthly mortgage escrow costs. Lenders collect these additional payments in an escrow account, typically on a monthly basis, in order to make sure you don't fall short of your annual tax and insurance obligations.

## What Other Expenses Does Homeownership Entail

It's important to recognize that the estimated total cost of your home purchase is only an estimate and not necessarily representative of future conditions. There are many factors that are not taken into account in the calculations we illustrated above; we include a few below for your consideration.

#### Taxes

While these fixed fees are charged regularly, they have a tendency to change over time, especially in large metropolitan areas like New York and Boston. New-home purchases often have their values reassessed within a year or two, which impacts the actual taxes paid. For that reason, your originally forecasted tax liability may increase or decrease as a result of new assessments.

#### HOA Dues

For buyers considering condos, homeowners associations can increase their monthly dues or charge special HOA assessments without warning. This can make up a large portion of your housing expenses, especially in large cities with high maintenance fees. You might also be subject to increased volatility in HOA fees if the community you live in has issues keeping tenants or a troubled track record.

#### Market Risk

The housing market varies by region and is cyclical, much like the stock market. There's always the risk of market value movements and insurance costs that might change over time. While real estate has always been considered one of the safest of investments, there's always a possibility that your home value will drop below the amount you paid for it. These risks are difficult to quantify but should be considered carefully before purchasing a home.

#### Maintenance Costs

Finally, typical mortgage expenses don't account for other costs of ownership, like monthly utility bills, unexpected repairs, maintenance costs and the general upkeep that comes with being a homeowner. While these go beyond the realm of mortgage shopping, they are real expenses that add up over time and are factors that should be considered by anyone thinking of buying a home.

## Calculating ARMs, Refinances and Other Mortgage Types

The equations that we've provided in this guide are intended to help prospective borrowers understand the mechanics behind their mortgage expenses. These calculations become more complicated if you're trying to account for ARMs or refinances, which call for the use of more specialized calculators or spreadsheet programs. You can better understand how these loan structures work by referring to one of our guides about mortgage loans below:

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