# How the USA and Canada Calculate Mortgage Payment

Mar 21, 2015

The USA and Canada each use a compound interest equation to amortize bank loans but differ in the compounding convention they each use for the amortization. As a result, the monthly mortgage payment in the USA will calculate higher than in Canada for exactly the same loan amount, interest rate and loan term.

Before showing you why that occurs though, let's take a quick look at what it means to compound the interest. Compound interest arises when interest is added to the principal (called compounding). 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

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

Say you borrow \$4,000 at 8% interest compounded every year all due and payable in two years. The amount due at the end of the first year would be \$ 4,320 (4000 x .08 = 320 + 4000) and at the end of the second year the amount would be \$ 4,665.60 (4320 x .08 = 345.60 + 4320).

Okay, now let me show you how each of the two countries compound their loans followed by an example and the formulation to illustrate it.

1. 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. 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.

### Example

Let's assume that we want to borrow a loan amount of \$100,000 at 7.00% interest rate that is fully amortized over 25 years. Here's the monthly principal and interest mortgage payment for each country.

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

Note: The monthly payment in the United States is higher than in Canada because the number of compounding periods per year is more frequent in the USA.

### Formulation

To make the calculation requires two steps. Bear in mind that we are using identical loans and only changing the compounding period that each country applies.

Step One
First, 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

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
Secondly, 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

result,

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

### So You Know

ProAPOD Agent 6 is the real estate software solution we recommend if you want the option to use either the USA or Canadian compound interest approach for your mortgage payment calculations.

James Kobzeff
Jim is a former realtor with over thirty years real estate investment property experience. He is the developer of ProAPOD's rental property analysis software solutions.