# How is Mortgage Interest Calculated in Canada?

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## Effective Annual Rate Calculator/Interest Rate Converter

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Applied Interest Rate
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Effective Annual Rate (EAR) is defined as the rate a lender would earn at the end of the year if they lend every interest or principal they receive with the same rate again. In other words, the EAR is the rate of interest when compounding is taken into account.

EAR is calculated using the effective annual rate formula,

This interest rate converter/calculator calculates the applied interest rate using the equivalence of Effective Annual Rates (EAR). The applied interest rate is the interest rate which has the same EAR at payment frequency as the nominal interest rate if payment was made at each compounding period.

Best 5-Year Fixed Mortgage Rates in Canada
Mortgage Term:
Fixed
Variable

Mortgage interest in Canada is calculated as a percentage of the unpaid principal balance of the mortgage loan. This percentage is known as the mortgage interest rate. The mortgage can have a fixed interest rate, meaning that it stays the same for the entire term of the mortgage, or it can have a variable interest rate. A variable interest rate fluctuates based on the lender’s prime rate changes. Canadian lenders' prime rate often changes based on changes in the Bank of Canada’s policy rate.

For example, to calculate the monthly mortgage interest on a specific loan, you can use the following formula:

Monthly Interest = (interest rate/12) x unpaid principal balance.

Numeric example: if you have a mortgage loan with an outstanding principal balance of \$300,000, an interest rate of 3% per year, and a term of 25 years, your monthly mortgage interest would be:

Monthly Interest = (0.03/12) x \$300,000 = \$750.

Remember that this is just the interest portion of your mortgage payment and does not include any payments toward the loan's principal balance.

It looks straightforward. Yet a small detail may mean that the interest rate you should use in this formula differs from the rate stated in your mortgage contract. This small complication is due to the potential difference between the compounding and payment periods.

## Compounding of Mortgage Interest in Canada

Canada’s Interest Act states the following about amortizing mortgages: “... the principal money and the rate of interest chargeable on that money, calculated yearly or half-yearly, not in advance.” As you can see, the interest can only be charged (or accumulated) yearly or semiannually for an amortizing mortgage. But mortgage payments are often made far more frequently.

Frequent mortgage payments benefit borrowers as borrowers can lower their total interest by making more frequent payments. They also help lenders because borrowers are less likely to default on periodic small payments than on infrequent large amounts. It is far easier to pay a portion of each paycheck to your mortgage lender than to save it over six months and make the payment semiannually.

For financial institutions to obey the Interest Act, in all Canadian fixed-rate mortgages, interest is compounded semiannually, but the borrower makes more frequent payments. Variable rate mortgage might compound semiannually or monthly. In each lending transaction, the more frequently the interest is charged (or compounded), the more beneficial it would be to the lender and the more costly it would be to the borrower.

In order to be fair, the interest which is charged every month or more frequently should be charged at a lower rate in order to have the same effect as the contract rate charged semi-annually.

If we denote the contract rate (which is compounded semi-annually) by i and the rate which is charged to customers (on a monthly basis) by r, these rates should both result in the same effective annual rate (EAR).

For semi-annual compounding, we would have

while for monthly compounding, we have

We expect the rate expressed in the contract and the rate paid by the borrower to result in the same EAR. Thus we must have

in other words,

This relation allows us to derive a monthly compounding rate r which is equivalent to the semi-annual compounding rate i.

This relationship can be easily generalized. If we have a rate, i, compounded m times each year; we can find the equivalent rate, r, which is compounded n times yearly. The relationship between these two rates is given by

In other words,

Best 5-Year Fixed Mortgage Rates in Canada
Mortgage Term:
Fixed
Variable

### Numerical Example:

Mr. and Mrs. Jones have qualified for a \$250,000 mortgage with a 5% per annum rate, compounding semi-annually. They plan to make weekly payments for this mortgage and want to know the interest they will pay for the first week.

Their stated rate i = 0.05, which is compounded twice each year. Thus m = 2. Each year contains 52 weeks, so we have n = 52. The weekly interest rate they are charged is

The interest they have to pay for the first week of their mortgage is 0.00095016699178 x \$250,000 = \$237.54.

## What Determines Mortgage Rates?

Mortgage rates are determined by several factors, including

1. The Bank of Canada’s policy rate: The Bank of Canada (BoC) sets a range for the overnight rate, the interest rate at which money is borrowed/lent against the security of government bonds overnight. When the BoC rate changes, so do the prime rate, affecting mortgage rates.
2. Inflation: Inflation can cause mortgage rates to increase, as lenders will charge higher interest rates to account for the fact that the money they lend will be worth less in the future.
3. The bond market: Lenders often bundle mortgages and create mortgage-backed securities (MBS). MBS are then sold to investors. The price of MBS determines the cost of funding mortgages for a lender. The price of MBSs are often tied to the performance of government bonds. In Canada, the most important government bonds are the 5-year bond and the 10-year bond. When bond prices rise, interest rates fall, and when bond prices fall, interest rates rise.
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