How mortgage interest is calculated
Mortgage interest is the cost you pay to borrow money for your home. In Canada, the amount of interest you pay depends on the principal (the amount you borrow), the interest rate, and the length of your amortization period. Lenders use a standardized formula to calculate your periodic interest and payment amount.
The standard mortgage payment formula is: Payment = P × r ÷ (1 - (1 + r)^(-N)), where P is the principal, r is the periodic interest rate, and N is the total number of payments. This formula ensures that each payment covers the interest due for that period and reduces the principal, so the loan is fully paid off by the end of the amortization period.
For example, a $300,000 mortgage with a 25-year amortization at 4% interest results in a monthly payment of $1,587.06, and the total interest paid over 25 years is $173,418.18.
- Principal is the amount you borrow.
- Interest rate is the annual percentage charged by the lender.
- Amortization is the total time to pay off the mortgage, typically 25 years.
- The payment formula allocates each payment between interest and principal.
How compounding affects Canadian mortgages
Compounding means that interest is calculated on both the original principal and any interest that has already accrued. In Canada, for fixed-rate mortgages, interest must be compounded semi-annually as required by the Interest Act. This means interest is added to the principal twice a year, even if you make monthly payments.
This semi-annual compounding makes the effective annual rate (EAR) slightly higher than the nominal rate. For example, a nominal rate of 5% compounded semi-annually results in an effective annual rate of approximately 5.06%. The formula for this is: EAR = (1 + rate/2)^2 - 1.
The effect of compounding is to increase the total interest paid over the life of the mortgage compared to simple annual compounding. Because interest accrues on interest, the effective rate is higher, and the total cost of borrowing rises. For variable-rate mortgages, the compounding frequency can vary by lender, so it's important to check your mortgage agreement.
- Fixed-rate mortgages compound semi-annually by law.
- Effective annual rate is higher than the nominal rate due to compounding.
- Compounding increases total interest paid over the amortization period.
- Variable-rate compounding may differ; check with your lender.
Fixed vs. variable interest rates explained
A fixed interest rate mortgage keeps the same interest rate for the entire term, which is typically 1 to 5 years. This means your payment amount stays predictable, but the rate is usually higher than a variable rate.
A variable interest rate can increase or decrease during the term, usually following changes in the prime rate. Variable rates are often lower than fixed rates initially, but they carry the risk of rising.
Lenders set your specific mortgage interest rate based on several factors, including the prime rate, posted rates, discounted rates, your credit history, and the term length. A better credit rating can help you qualify for a lower rate.
- Fixed rate: constant for the term, usually higher than variable.
- Variable rate: can change with the prime rate, may be lower initially.
- Your credit rating affects the rate you are offered.
Sources: Financial Consumer Agency of Canada, Bank of Canada
How payment frequency affects interest
The frequency of your mortgage payments can affect the total interest you pay over the life of the loan. Making payments more frequently, such as bi-weekly instead of monthly, means you make 26 half-payments per year, which is equivalent to 13 full monthly payments. This extra payment reduces your principal faster and lowers the total interest charged.
For example, a borrower with a $300,000 mortgage at 4% interest over 25 years will pay less total interest if they make accelerated bi-weekly payments compared to monthly payments, because the principal is reduced more quickly.
The interest calculation for each payment period uses the periodic rate derived from the effective annual rate. To convert the annual rate to a monthly rate for monthly payments, you first calculate the EAR from the nominal rate using semi-annual compounding: EAR = (1 + nominal/2)^2 - 1. Then, the monthly periodic rate is r = (1 + EAR)^(1/12) - 1. This sequence ensures that the semi-annual compounding is accounted for in each monthly payment.
- Bi-weekly payments can reduce total interest by making an extra payment each year.
- The periodic interest rate is calculated from the effective annual rate.
- Faster principal reduction means less interest accrues over time.
Using the mortgage payment formula
You can calculate your mortgage payment using the standard formula: Payment = P × r ÷ (1 - (1 + r)^(-N)). To use it, you need three inputs: the principal (P), the periodic interest rate (r), and the total number of payments (N).
For a monthly payment schedule, the periodic rate is derived from the effective annual rate, which accounts for semi-annual compounding. Then the monthly periodic rate is r = (1 + 0.0404)^(1/12) - 1 = 0.003274. The total interest over the amortization period is $1,587.06 × 300 - 300,000 = $173,418.18.
This example demonstrates the step-by-step application of the formula, ensuring you can replicate the calculation with your own mortgage details.
- Inputs: principal, periodic rate, number of payments.
- Derive the periodic rate from the EAR, which includes semi-annual compounding.
Frequently asked questions
Is mortgage interest calculated annually in Canada?
No, mortgage interest is not calculated annually. Fixed-rate mortgages in Canada compound semi-annually as required by the Interest Act, meaning interest is added to the principal twice a year. However, each payment is calculated using a periodic rate that reflects this semi-annual compounding, so the interest you pay each month is based on the remaining principal and the effective annual rate. Variable-rate mortgages may compound differently, potentially monthly, depending on the lender.
Sources: WOWA.ca, nesto.caHow does a variable rate mortgage work?
A variable-rate mortgage has an interest rate that can increase or decrease during the term, usually following changes in the prime rate. Your payment amount may stay the same for a period, but the portion going to interest and principal changes as the rate changes. Variable rates are often lower than fixed rates initially, but they carry the risk of rising interest costs. The compounding frequency for variable-rate mortgages can vary by lender, so it's important to check your terms.
Sources: Financial Consumer Agency of Canada, nesto.caWhat is the difference between the interest rate and the effective rate?
The interest rate, or nominal rate, is the stated annual rate on your mortgage. The effective annual rate (EAR) accounts for compounding and is higher than the nominal rate. For example, a nominal rate of 5% compounded semi-annually results in an EAR of approximately 5.06%. The EAR is used to calculate the periodic interest rate for your payments, ensuring you pay interest on the interest that has already accrued.
Sources: nesto.caDoes making payments bi-weekly save interest?
Yes, making bi-weekly payments can save interest compared to monthly payments, because you make an equivalent of 13 full payments each year instead of 12. This extra payment reduces your principal faster, so less interest accrues over the life of the mortgage. The exact savings depend on your interest rate and amortization period.
Sources: Financial Consumer Agency of CanadaHow can I lower my mortgage interest rate?
Several factors can help you secure a lower mortgage interest rate. Improving your credit rating can qualify you for a better rate because lenders use credit history to assess risk. Shopping around and negotiating with lenders can also help you find discounted rates. Additionally, choosing a shorter term or a variable rate may result in a lower initial rate, but consider the trade-offs. The Bank of Canada's policy rate influences market rates, so monitoring economic conditions can inform your timing.
Sources: Financial Consumer Agency of Canada, Bank of CanadaSources
- Interest on mortgages - Canada.ca — Financial Consumer Agency of Canada
- Notes on Canadian interest rates - Bank of Canada — Bank of Canada
- How is Mortgage Interest Calculated in Canada? | WOWA.ca — WOWA.ca
- Mortgage Principal and Interest Explained - nesto.ca — nesto.ca
- Canada Mortgage Payment Calculator - NerdWallet — NerdWallet