# Mastering Mortgage Math: A Step-by-Step Guide to Calculating Different Mortgage Payments

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| 31 July 2023
Reviewed, 31 July 2023
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Are you a first-time homebuyer trying to navigate the complex world of mortgage payments? Or maybe you’re a seasoned homeowner looking to refinance and want to ensure you get the best deal. The world of mortgages and trying to make sense of mortgage math can get confusing even for the most analytical minds.

Whether you’re a numbers whiz or just trying to make sense of how your payments are calculated, this comprehensive guide will walk you through the step-by-step process of calculating different mortgage payments. By the end of this guide, you will better understand how payments are calculated so you can take control of your finances.

## Key Takeaways

• A mortgage is a loan used to purchase a home or property and consists of principal and interest components.
• Mortgage calculators simplify calculations, allowing users to experiment with different scenarios and financial outcomes.

## Understanding the Basics of Mortgage Math

When it comes to mortgage math, starting with a solid foundation and understanding the basics will help you grasp more complex calculations. A mortgage is a loan used to purchase a home or property. The borrower agrees to repay the loan, plus interest, over a set period, called the amortization.

The monthly mortgage payment consists of two main components: principal and interest. The principal is the initial amount borrowed, while the interest is the cost of borrowing money from the lender.

You need the mortgage amount, interest rate, and amortization to calculate your monthly mortgage payment. The mortgage amount is the total value, while the interest rate is the percentage the lender charges for borrowing the money. The amortization period is the length of time based on what you selected when obtaining your mortgage. On prime mortgages, 25 years is generally the most popular option among Canadians, though you can have an amortization of up to 30 years, depending on your down payment amount.

Subprime and private mortgages are available with higher amortizations or interest-only payments (never required to make payments to the principal balance). These types of mortgages generally require a bigger down payment and come with higher rates as the lender is willing to take on more risk to carry the borrower’s mortgage.

Armed with this information, you can use a mortgage calculator or a mathematical formula to determine your monthly payments.

Calculating your total interest paid over the life of the mortgage can also be important. The total interest tells you how much money you’ll pay in interest over your mortgage’s entire amortization. By understanding the impact of interest, you can make better decisions about your mortgage, such as whether it’s cost-effective to refinance for a lower interest rate before your mortgage term has ended.

## Different Types of Mortgage Payments

Mortgages come in two types: fixed-rate and variable-rate, and each option has its advantages and disadvantages. The mortgage type you choose will affect your mortgage payments.

### Fixed-Rate Mortgages

Fixed-rate mortgages have a fixed interest rate that remains the same throughout the mortgage term. This means your interest rate won’t change until the end of each term when you come up for renewal. Payments on fixed-rate mortgages will remain the same for the duration of the mortgage term. Some lenders may offer the option to early renew or blend & extend your fixed-rate mortgage before the completion of your term.

### Variable Rate Mortgages

Variable-rate mortgages have fluctuating interest rates, and monthly payments can either remain the same or change depending on which variable-rate mortgage option you choose.

Variable-rate mortgages (VRM) have fixed payments that do not change with changes in the interest rate over the term. If interest rates increase, more of your mortgage payment goes toward the interest portion and less to the principal. If rates decrease, more of your payment will go toward the principal portion as less is needed for the interest. Payments on VRM mortgages will remain the same for the mortgage term, regardless of any changes to interest rates.

Adjustable-rate mortgages (ARM) have adjustable payments that change with changes to the interest rate over the term. This means that the interest portion of your payment will adjust and either increase or decrease alongside changes to the lender’s prime rate. With adjustable-rate mortgages, your monthly mortgage payments could increase or decrease as often as interest rates change over the term.

## Calculating Monthly Mortgage Payments

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

M = Monthly mortgage payment

P = Principal (total mortgage amount)

i = monthly interest rate (annual interest rate divided by 12)

n = Total number of monthly payments (mortgage amortization in years multiplied by 12)

For example, let’s say you have a \$500,000 mortgage with an interest rate of 5.14% and an amortization of 25 years. To calculate your monthly payment, you would plug in the values into the formula as follows:

M = 500,000 [(0.0514/12)(1 + (0.0514/12))^300] / [(1 + (0.0514/12))^300 – 1]

M = 500,000 [0.00428333(1 + 0.00428333)^300] / [(1 + 0.00428333)^300 – 1]

M = 500,000 [0.0154403705] / [2.60475856433]

M = 2963.87748013

Your monthly mortgage payment is approximately \$2,964. Remember to always round up to ensure you have budgeted enough funds to cover the monthly payment, as rounding will impact the output of the equation.

Using a mortgage payment calculator can simplify this process. Many online calculators allow you to input your mortgage amount, interest rate, and amortization, and they will calculate your monthly payment. This can be helpful if you’re uncomfortable with complex mathematical formulae or want to quickly and easily compare different mortgage scenarios.

## Using Mortgage Calculators to Simplify the Process

Mortgage calculators can simplify calculations and provide a more accurate estimation. They allow you to experiment with different mortgage amounts, interest rates, and amortizations to see how they affect your monthly payment and total interest costs. By inputting various scenarios, you can compare the outcomes and find ways to save interest-carrying costs on your mortgage.

### FTHB Mortgage Payment Calculator

Our mortgage payment calculator can help first-time homebuyers (FTHB) input details of the home they wish to purchase and estimate monthly mortgage payments giving them a head start on budgeting for this expense.

You can use the calculator to run scenarios based on the home’s asking price, the amount you have saved for a down payment, the amortization period, and payment frequencies. Run test scenarios to see how your down payment affects the amount you need to borrow, whether mortgage default insurance (CMHC) will be required, and how this could impact your mortgage payments.

### Renewal  Mortgage Payment Calculator

Our mortgage renewal calculator can make it easier for those homeowners coming up for renewal to estimate and run scenarios and calculate their future mortgage payments.

You can use our calculator to run scenarios by entering the current value of your home, the balance remaining on your mortgage, the remaining amortization, and payment frequency.  Run test scenarios to see how changing the payment frequency to an accelerated option can save interest-carrying costs and pay off your mortgage sooner by reducing amortization.

### Refinance Mortgage Payment Calculator

Our mortgage refinance calculator makes it easy for those looking to refinance their mortgage to run scenarios and calculate future mortgage payments.

You can use the calculator to run scenarios based on the current value of your home, the balance remaining on your mortgage, the remaining amortization, payment frequency, and mortgage rate. By selecting the purpose of the refinance (lower mortgage payments, access equity, or change amortization), you can quickly and easily compare the total interest you will pay over the term with your mortgage. This cost analysis will allow you to quickly compare if a refinance makes sense for your situation and comes with cost-saving benefits.

## Understanding the Impact of Interest Rates on Mortgage Payments

Interest rates play a significant role in determining your mortgage payment and the overall cost of homeownership. Even a small change in interest rates can substantially impact your monthly payment and the total interest paid over the life of the mortgage.

Various factors influence interest rates, including economic conditions, inflation, and monetary policies. When interest rates are low, borrowing becomes more affordable as the cost of borrowing decreases. This means your monthly mortgage payment will be lower, allowing you to afford a more expensive property or reduce your monthly mortgage payments.

On the other hand, when interest rates are high, borrowing becomes more expensive as the cost of borrowing increases. This leads to higher monthly mortgage payments and potentially limits your purchasing power. Additionally, high-interest rates can result in higher total interest paid over the life of the loan, increasing the overall cost of homeownership.

To illustrate the impact of interest rates, let’s use figures from our monthly mortgage calculation above. A \$500,000 mortgage with a 25-year amortization with an interest rate of 5.14% has an approximate monthly payment of \$2,964. If the interest rate increases to 6.14%, the monthly payment would increase to approximately \$3,266. The 1% increase in the interest rate equates to an additional \$302 per month.

To simplify this math further, consider that each \$100,000 mortgage balance over a 25-year amortization has a \$15 increase each time interest rates are bumped up by 25 bps (a basis point equals 0.01%) – the same as 0.25%.

This example demonstrates the importance of shopping around for the best interest rates and considering the long-term financial implications. Even a slight reduction in interest rates can save you a significant amount of money over the life of your mortgage.

## Exploring the Benefits of Making Extra Mortgage Payments

Making extra mortgage payments can be a smart financial move that can save you thousands of dollars in interest-carrying costs and help you pay off your mortgage faster. By allocating additional funds toward your principal balance, you reduce the total interest you will pay over time and reduce your amortization.

There are a few strategies you can leverage to make extra mortgage payments. One common approach is to make a prepayment on the principal portion of your mortgage, which depending on your lender’s criteria, can either be made as a lump sum or by dividing it into smaller payments over the year. This can help you pay off your mortgage faster and save on interest.

Another strategy is to round up your payment to the nearest hundred or even thousand. For example, if your monthly payment is \$1,232, you could round it up to \$1,300. The additional amount directly reduces the principal balance, total interest paid, and amortization.

The final strategy is to set up your payments using an accelerated payment frequency. Choosing an accelerated bi-weekly payment instead of bi-weekly will increase the total payments you make in a year from 24 to 26. Choosing an accelerated weekly payment instead of weekly will increase the total payments you make in a year from 48 to 52. Accelerated payments reduce your amortization and interest paid over the life of the mortgage since you are making a few extra payments per year.

Before making any additional mortgage payments, check with your lender to see what prepayment privileges are available on your mortgage to avoid potential penalties. Some lenders will charge fees for paying off too much of the principal or may limit the number of extra payments you can make per year. Some lenders will even limit your prepayment privilege to be exercised only on your mortgage anniversary date, limiting your ability to make a prepayment when you receive your bonus or get a windfall.

### How are mortgage payments calculated?

Mortgage payments are made up of 2 parts: principal and interest. The principal is the amount you’ve borrowed to purchase your home, and the interest is the cost the lender charges for borrowing money. Your mortgage payment is the sum of these two amounts divided by the number of payments over your mortgage term.

### What is amortization?

Amortization refers to the life of the mortgage, which is the time it takes to repay the principal and interest you borrowed. Typically, if your down payment is less than 20%, the longest you can amortize is 25 years.

### How frequently can you make mortgage payments?

Mortgage payments can be made weekly, bi-weekly, or monthly. You can also make payments on an accelerated bi-weekly or weekly basis to reduce interest-carrying costs and the time it will take to pay off your mortgage.

## Final Thoughts: Mastering Mortgage Math for a Smarter Home-Buying Experience

Understanding mortgage math or how to use mortgage calculators to your advantage is a must for anyone looking to purchase a home or with an existing mortgage. Utilizing mortgage calculators and exploring the impact of interest rates on your mortgage payments can help you determine what works best for your financial situation and help you find ways to save money. By understanding the basics and how to calculate monthly payments, you can put this knowledge to work and find ways to compare and save on your mortgage.