# Demystifying Mortgage Calculations in the US and Canada

Apr 1
20:12

2024

James Kobzeff

Understanding the nuances of mortgage calculations can be a daunting task, especially when comparing the systems in the United States and Canada. The key distinction lies in the frequency of compound interest, which significantly impacts the overall payment amounts. This article will guide you through the differences, provide the formulas needed for accurate calculations, and offer insights into the tools available for managing these financial decisions.

## The Essence of Compound Interest

Compound interest is the financial principle where interest is charged on both the initial principal and the accumulated interest from previous periods. This contrasts with simple interest, where interest is only calculated on the principal amount. The frequency of compounding—daily, monthly, or annually—can greatly affect the total amount of interest paid over the life of a loan.

For instance, a \$100,000 loan with a 7.00% interest rate over 25 years would require a monthly payment of \$706.78 if compounded monthly, but only \$700.42 if compounded semi-annually. The more frequent the compounding, the higher the payment, as the interest is calculated more often.

## US vs. Canadian Mortgage Compounding

In the United States, mortgages typically compound monthly, leading to higher monthly payments compared to Canadian mortgages, which compound semi-annually. This difference in compounding frequency can result in noticeable variations in payment amounts over the duration of the loan.

### The Calculation Formula

To accurately calculate mortgage payments, you must determine the interest rate per payment period. The formula is as follows:

Interest Rate Per Payment = ((1 + annual interest rate / compounding periods)^(compounding periods / payment periods per year)) - 1

For a 7.0% annual interest rate with twelve payments per year, the interest rate per payment would be:

• For semi-annual compounding (Canada): ((1 + 0.07 / 2)^(2 / 12)) - 1 = 0.575%
• For monthly compounding (USA): ((1 + 0.07 / 12)^(12 / 12)) - 1 = 0.583%

The difference is subtle but significant over time.

### Calculating Loan Payments

To calculate the loan payment, you need the interest rate per month, the loan amount, and the total number of payments (nper). The formula is:

Loan Payment = -PMT(interest rate per month, nper, loan amount)

For a \$100,000 loan over 25 years (300 payments):

• Canada: -PMT(0.00575, 300, 100,000) = \$700.42
• USA: -PMT(0.00583, 300, 100,000) = \$706.78

## Tools for Mortgage Calculation

There are various methods to compute mortgage payments, including online mortgage calculators, spreadsheet programs like Microsoft Excel, and specialized real estate investment software. Utilizing these tools can simplify the process and ensure you have a clear understanding of your financial commitments.

By grasping the differences in mortgage calculations between the US and Canada, and learning how to apply the correct formulas, you can make informed decisions regarding your mortgage options.

While the focus is often on interest rates and compounding periods, other factors such as amortization periods, down payment requirements, and mortgage insurance can also vary between the two countries and influence the total cost of a mortgage. For example, in Canada, homebuyers with less than a 20% down payment must purchase mortgage loan insurance, which can add to the overall cost of the loan.

According to the Canadian Mortgage and Housing Corporation (CMHC), the average amortization period for insured mortgages in Canada was 25 years as of 2020. In contrast, the most common mortgage term in the United States is 30 years, according to the U.S. Bureau of Labor Statistics.

Understanding these additional aspects, along with the primary calculation differences, is crucial for anyone considering a mortgage in either country. For more detailed information on mortgage calculations and comparisons, you can visit authoritative sources such as the Consumer Financial Protection Bureau in the US and the Canadian Mortgage and Housing Corporation in Canada.

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