The way mortgages are calculated in Canada is vastly different from how they are calculated here in the US. The major difference being on the way compound interest is calculated. But to more clearly understand, we should start at the beginning.
Compound Interest
The underlying assumption of compound interest is that interest is earned on interest. Therefore, with compound interest you apply the interest rate to the original principal as well as to all accumulated interest. This is different from simple interest, where the interest rate is applied only to the original principal amount.
Hence, the higher the compounding rate and the more frequent the compounding (known as the compound period), the larger the resulting mortgage payment.
For example, assume a loan amount of $100,000 at 7.00% interest rate amortized over 25 years. The monthly mortgage payment is $706.78 when compounded monthly and $700.42 when compounded semi-annually. As you can see, the payment is higher when the compound period is monthly rather than semi-annually because monthly compounding is clearly more frequent than semi-annual compounding.
Okay, let's consider the difference between US and Canadian mortgages.
Mortgages in the United States are compounded monthly whereas mortgages in Canada are compounded semi-annually. This means that monthly mortgage payments on identical loans are higher in the United States than they are in Canada because the number of compounding periods per year is higher (as our example above reveals).
The Formula
To calculate the mortgage payment in either country correctly, you must first calculate the interest rate per payment. Here's the formula:
((1+interest rate/compound period)^(compound period/periods per year))-1
For example, assume an annual interest rate of 7.0%, and twelve periods per year. The calculation for the interest rate per payment for semi-annual compounding (as in Canada) is:
((1+0.07/2)^(2/12))-1 = 0.575%
The calculation for the interest rate per payment for monthly compounding (as in the USA) is:
((1+0.07/12)^(12/12))-1 = 0.583%
Are you able to see the difference? With semi-annual compounding, the compound period is 2 (twice annually) whereas with monthly compounding the compound period is 12 (twelve times annually).
Okay, now let's calculate each country's loan payment where:
rate = interest rate per month (0.575% or 0.583%)
loan amount = $100,000
nper = total number of payments for the loan (300, or 25x12)
Formula: -PMT(rate,nper,loan amount)
Canada: -PMT(.00575,300,100000) = $700.42
USA: -PMT(.00583,300,100000) = $706.78
How to Make the Calculation
You can use a mortgage calculator, a spreadsheet program, or quality real estate investment software to calculate mortgage payment.
Whatever method you use, though, hopefully by knowing the difference between how mortgages are treated here in the United States versus those in Canada, as well as how to compute them, you will get the results you desire.
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