# How USA and Canada Compound Interest Equations Differ Both the USA and Canadian real estate sectors routinely issue mortgages using a compound interest equation to determine the monthly principal and interest payment.

But the monthly mortgage payment calculated for loans in the USA is vastly different from loans issued in Canada. The major difference resting solely on the way each of the two countries calculate for compound interest.

In this article we’re going to discuss both methods so you can see how each compounds loan interest and why US and Canadian mortgages differ.

The underlying assumption of compound interest – unlike simple interest – is that interest is earned on interest.

In other words, with simple interest the interest rate is applied only to the original principal amount, whereas with compound interest the interest rate is applied to the original principal as well as to all accumulated interest.

Hence, the higher the compounding rate and the more frequent the compounding (or the compound period), the larger the resulting mortgage payment.

#### USA Compounding

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.

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.

##### Result

The monthly mortgage payments on a loan issued in the United States identical to a loan issued in Canada with be higher because the number of compounding periods per year are more frequent in the US than in Canada.

For example, assume a loan amount of \$100,000 at 7.00% interest rate fully amortized over 25 years. In the US – where interest is compounded every month – the monthly mortgage payment with principal and interest is \$706.78. When compounded semi-annually, as in Canada, the monthly mortgage payment with principal and interest is \$700.42.

#### How to Apply

Okay, let’s look at the two steps required to compute the monthly payment for each country. Bear in mind that we are using identical loans for each country (as shown above) and the only difference concerns the compounding period each country uses.

##### Step One

We must calculate the interest rate per payment for each of the two mortgages.

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

or,

USA: ((1+0.07/12)^(12/12))-1 = 0.583%

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.

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

or,

USA: -PMT(.00583,300,100000) = \$706.78 