How to calculate mortgage payments—without a mortgage payment calculator

But have you ever wondered how mortgage payment calculators work? We break down the math to help illustrate why you end up with that specific payment amount.

Maybe you’d like to run the numbers the ol’ fashioned way with a pen and paper (or the calculator app on your phone), or maybe you’d just like a better understanding how the number that your monthly budget likely revolves around is determined. Whatever your reason, read on to see how to calculate your mortgage payments yourself—no mortgage calculator required. 

What you’ll need to calculate your mortgage payments

To get started, you’ll need a regular calculator, since we’ll be crunching numbers. Also, have three pieces key of information ready, since you’ll need to plug them into the mortgage payment formula (below). Keep in mind that this formula will only calculate your monthly mortgage payment—bi-weekly or accelerated bi-weekly payments, for example, would be calculated differently. The three pieces of info you’ll need to know are: 

1. The mortgage principal

This refers to the total amount that you borrowed. To determine your mortgage principal—the outstanding balance on the amount that you borrowed—subtract the down payment from the total purchase price of the home. For example, a down payment of $120,000 on a $600,000 home would leave you with $480,000 in mortgage principal. When you make your regular mortgage payments, part of the money goes towards the principal and part of it goes towards paying interest on the loan. 

Mortgage principal = purchase price – down payment 
Mortgage principal = $600,000 – $120,000
Mortgage principal = $480,000

2. The monthly interest rate on your mortgage

Lenders like to use annual interest rates in their mortgage contracts. This means you’ll have to divide the quoted rate by 12 to determine your monthly interest rate, before inputting it into the mortgage payment formula. (Remember: This will help you figure out how much you will pay every month; for bi-weekly payments, this formula doesn’t work.) 

For example, let’s say you’re offered a mortgage rate of 2.69%. To avoid ending up with a number that’s far greater than it should be, you’ll need to convert the percentage into a decimal by dividing the number by 100. Then, you’ll need to divide the result by 12. This leaves you with a monthly interest rate of 0.00224. Note: To make life easy (and the numbers less cumbersome), we’ve rounded to five decimals. 

Monthly interest rate = annual interest (%) / 100 / 12 months 
Monthly interest rate = 2.69 / 100 / 12 
Monthly interest rate = 0.00224 

3. The number of payment periods

The total number of mortgage payments it will take to pay off the mortgage in its entirety, based on the amortization period. Again here, lenders use annual terms to describe the length of time you will carry your mortgage loan (known as the amortization period). In Canada, lenders typically offer amortization periods of five to 25 years. This isn’t the same as your mortgage term, which is the duration of your mortgage contract. You will usually complete several mortgage terms before paying off your mortgage in full. 

Before completing the next step using the mortgage payment formula, make sure you have converted your amortization period into a total number of payment periods. To do that, multiply the number of years in your amortization by 12. For example, a 25-year mortgage will leave you with 300 payment periods before you have paid off your mortgage. 

Payment periods = number of years x 12 months
Payment periods = 25 x 12
Payment periods = 300

Using the mortgage payment formula

Now that you have those three numbers in hand—your mortgage principal, your monthly interest rate and your number of payment periods—complete the formula below. For simplicity, we’ve attributed a symbol for each of the three inputs used in the formula. 

Monthly payment = P x (I x (1+ I)^N ) / ((1 + I)^N – 1)

P = Mortgage principal
I = Monthly interest rate
N = Number of payment periods

Simply swap out the variables with your own inputs and complete the calculation. Note, you’ll want to follow the same sequence of calculations as we do in order to get the correct result. 

1. Calculate the parentheses first (don’t forget the rules of PEMDAS from school: parenthesis, exponents, multiplication, division, addition, then subtraction), starting with the parentheses within the parentheses. 
2. Calculate the exponents (^). An exponent represents a series of multiplications. For example: 2^2 = 2 x 2 = 4 and 2^3 = 2 x 2 x 2 = 8. 
3. Calculate the remaining multiplications and divisions. 

Keeping with the example used above, let’s say you have enough saved for a 20% down payment ($120,000) on a $600,000 home, amortized over 25 years at a rate of 2.69%. In this case, your inputs are: 

P = 480,000
I = 0.00224
N = 300

Now let’s complete the equation by replacing the variables in the formula with the inputs:

Monthly payment = P x (I x (1+ I)^N ) / ((1 + I)^N – 1)
Monthly payment = 480,000 x (0.00224 x (1 + 0.00224)^300) / ((1+0.00224)^300 – 1)
Monthly payment = 480,000 x (0.00224 x 1.00224^300) / (1.00224^300 – 1)
Monthly payment = 480,000 x (0.00224 x 1.95667) / (1.95667 – 1)
Monthly payment = 480,000 x 0.00438 / 0.95667
Monthly payment = 2,102.4 / 0.95667
Monthly payment = 2,197.62

The answer represents the dollar amount of your monthly mortgage payments: $2,197.62

Inputting the same three pieces of information (without adjusting them for the formula) into a mortgage payment calculator will give you a slightly different result: $2,196. That’s because we’ve rounded our numbers to the fifth decimal point. Using a smaller or larger number of decimal points will yield different answers and may not precisely match the formula used by a mortgage payment calculator. 

Great, I’ve figured it out. Now what? 

If you’ve made it this far into this article, thank you. You likely see the value in crunching the numbers yourself. That’s great—you understand how calculators use your information to come up with the values they give you. 

But unless you find yourself on an island with not even a bar of internet access, you’ll probably want to use an online mortgage payment calculator if you have multiple scenarios to run through. The results will be more exact, and you’ll receive other important information based on the same inputs, such as how much you’ll need to pay in land transfer tax or mortgage default insurance fees (for down payments of less than 20%). 

Let’s be clear: Doing the math can be rewarding (and fun, if you’re into that kind of thing). But mortgage payment calculators allow you to do the same calculations quickly and easily, so you can compare different mortgage scenarios without all the pen-and-paper work.

More on mortgages:

• Every mortgage calculator you will ever need
• What’s the best mortgage for first-time home buyers?
• How much mortgage can I afford?
• Should you pay off your mortgage early?
• Home-financing tips for 5 types of buyers

About Justin Dallaire

Justin Dallaire is the senior editor at MoneySense.ca. He was previously the associate editor at Strategy magazine and has contributed to publications including The Walrus and TVO.org.

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