Formula to Calculate Mortgage Payments
If you're considering refinancing your mortgage or purchasing a new home, you can calculate your monthly mortgage payments using a specific calculation formula. For this formula you will need some basic numbers that are available in your mortgage documents.
The Formula
To calculate a mortgage payment for a fixed-rate mortgage, you will need to know your principal amount, interest rate, and length of loan:
- Principal amount: This is the amount of the mortgage or amount you want to borrow. In the example below, this amount is $100,000.
- Interest rate: This is the interest rate the financial institution or bank is charging. In the example below, this rate is 5%.
- Length of loan: This is the term or number of years of the loan. In the example below, the term is 15 years.
There are a set of standard abbreviations for these amounts and the mathematical processes used in these calculations:
Abbreviation | Represents |
APR | Annual Percentage Rate |
i | Interest Rate in Decimal Form |
I | Monthly Interest Rate |
PF | Payment Frequency |
n | Number of Payments |
L | Length of Loan |
T | Term of Loan |
M | Monthly Mortgage Payment |
P | Principal Amount |
/ | Division Symbol |
x | Multiplication Symbol |
Step 1: Convert Interest Rate into Decimal
The first step to calculating monthly mortgage payments is to convert the APR into a decimal fraction. To do so:
i = APR/100
For example, if you have a 5% interest rate: 5/100 = .05. In this example, therefore, i = .05
Step 2: Calculate Monthly Interest Rate
Next, determine the monthly interest rate. To do so, divide the decimal interest rate calculated in step one by payment frequency:
I = i/PF
If the loan must be paid every month in a year, 12 is the payment frequency. For example: .05/12 = .004167. In this example, therefore, I = .004167.
Step 3: Determine Total Number of Payments
The third step to calculating mortgage payments is to determine how many payments you will make over the life of the loan. To do so, multiply the length of the loan by payment frequency:
n = L x PF
For example, if you have a 15-year loan and make monthly payments: 15 x 12 = 180. Therefore, over the entire life of your mortgage, you would make 180 payments. In this example, therefore, n = 180.
Step 4: Calculate the Term
Fifth, calculate the term of the mortgage. The formula for this calculation is:
T = (1 + I)^{n}
Using the example of 0.004167, the calculation would be: 1 + 0.004167 = (1.004167)^{180} = 2.11383. In this example, therefore, T = 2.11383.
Step 5: Calculate Monthly Mortgage Payment
Finally, it is time to calculate the total amount of monthly mortgage payment. Assuming that interest is compounded monthly, for a fixed-rate mortgage, the formula is:
M = P (I x T) / T -1)
In this example: 100,000 [(.004167 x 2.11383) / (2.11383 - 1)] = 100,000 (.0088083 / 1.11383) 100,000 x .0079081 = 790.81. Therefore, in this example: M = $790.81.
Determine Overall Interest
If you want to know how much interest you'll pay over the life of the loan, multiply the amount of your monthly payment by the term of the loan and then subtract the principal. For example: $790.81 multiplied by 180 payments (15 years) equals $142,345.80 minus the loan principal of $100,000 equals $42,345.80. Therefore, in the 15 years of the loan, you'll pay about $42,345 in interest.
If You Want to Pay More
Making a larger-than-required mortgage payment or additional payments can reduce the amount of interest you pay on the loan. Several online calculators help you determine how making an additional payment will affect your loan:
- Ultimate Calculators: In addition to the basics of your loan, this "ultimate" calculator allows you to input a custom payment amount, or provide a lump sum payment amount or double-up payment amount as you would like. It also allows users to input an annual interest rate increase, which may assist with calculating payments and savings for an adjustable-rate mortgage. Once provided, the calculator provides you with information about how many payments are required with the additional payments and how much less you will pay in interest due to the additional payments.
- Free Online Calculator Use: This extra payment calculator allows users to input an additional amount they will pay each month or an additional one-time payment. It provides a payoff comparison detailing the number of months you will pay on the mortgage and the amount of interest you will pay.
Calculator for Computing Monthly Payment
This amortization calculator gives you a simple way to estimate your monthly payment:
Calculating Your Payment
Calculating your mortgage payment is made easier by breaking the formula provided above into several steps, as is shown. Determining the amount you will pay each month helps you determine whether you can afford to borrow the full amount offered or purchase the house with which you've fallen in love.