Why the Monthly Mortgage Payment Calculates Higher in the USA than in Canada

The USA and Canada each use a compound interest equation to amortize bank loans. That means that each country charges interest on the principal amount of the the loan as well as on any accrued interest. So lenders in both countries are the same in that they equally compound interest on the loans they make, and thus, each are equally charging the borrower "interest on the interest" for the loan.

Where they differ, however, is in the compounding convention they use for the amortization. And as we'll see, this will explain why the monthly mortgage payment in the USA will calculate higher than in Canada for exactly the same loan amount, interest rate, and term.

Fair enough. So let's dig in.

Compound interest arises when interest is added to the principal. In other words, when you borrow money from a bank with compound interest, you'll not only be charged interest on the principal amount of the loan, but also on any accrued interest. And that's why it's referred to as, "interest on the interest."

Here's a very simple example just to give you the idea.

Say you borrow $100,000 at 8% interest compounded annually all due and payable in two years. The ending balance at the end of the first year would be $108,000 (100,000 x .08 = 8,000 + 100,000), and at the end of the second year it would be $116,640 (108,000 x .08 = 8,640 + 100,000). In other words, whereas the interest was charged only on the original principal amount ($100,000) for the first year, it was then charged on the original principal amount plus the accrued interest ($108,000) in the second year.

Okay, now let me show the compounding convention each of the two countries uses that ultimately explain why the monthly mortgage payment calculates higher in the USA than in Canada.

1. USA. Mortgages in the United States are compounded monthly. That means that the interest rate is applied to the original principal of the loan as well as to all accumulated interest on a monthly basis.
2. Canada. Mortgages in Canada are compounded semi-annually. That means that the interest rate is applied to the original principal of the loan as well as to all accumulated interest every six months.

As you can see, the monthly mortgage payment calculates higher in the USA than in Canada because the number of compounding periods per year is more frequent in the USA (12 as opposed to 2).

How much higher? Let me show you. Let's assume a loan amount of $100,000 at 7.00% interest rate and fully amortized over 25 years. Here's the monthly principal and interest mortgage payment for each country.

1. USA = $706.78
2. Canada = $700.42

Okay, now let me show you the formulation. Bear in mind that we are using identical loans and only changing the compounding period that each country applies.

Step One
Calculate the interest rate per payment for each of the two country's mortgages using the following formula:

Interest Rate Per Payment = ((1+interest rate/compound period)^(compound period/periods per year))-1

Result,
USA: ((1+0.07/12)^(12/12))-1 = 0.583%
Canada: ((1+0.07/2)^(2/12))-1 = 0.575%

Note: If you carefully examine both results above you will see that the first part of the formula for the USA there is a compound period of 12 (signifying monthly compound interest), and for Canada a compound period of 2 (signifying semi-annual interest compounding).

Step Two
Calculate each country's monthly loan payment using the following formula:

Monthly Payment = -PMT(rate,nper,loan amount)

where,
rate = interest rate per month
nper = total number of payments for the loan
loan amount = loan amount

Result,
USA: -PMT(.00583,300,100000) = $706.78
Canada: -PMT(.00575,300,100000) = $700.42

And there you have it. A simple illustration that explains why the monthly mortgage payment calculates higher in the USA than in Canada. Hope it helps.

Here's to your real estate investing success.

So You Know

The following ProAPOD software solution is our recommendation if you want the option to use the Canadian compound interest approach for the mortgage payment calculations in your rental property analysis.