🏦 Loan amortization calculator

Amortization is based on a classic mathematical formula that calculates a constant periodic payment that fully repays the capital over the planned period, while paying the interest owed each period on the remaining balance. The basic formula is:

where P is the principal borrowed, r is the periodic interest rate, and n is the total number of payments. For a Canadian mortgage, the periodic rate must be adjusted from the nominal annual rate compounded semi-annually, giving r = (1 + i/2)^(2/m) − 1, where i is the posted annual rate and m is the number of payments per year (12 monthly, 26 bi-weekly, 52 weekly).

Principal vs interest breakdown

Each payment contains two parts: the interest portion is calculated on the remaining balance at the start of the period (balance × r), and the principal portion is what remains of the payment after paying interest. At the start of the amortization, the balance is high, so interest dominates; as the balance decreases, the principal portion grows and the interest portion shrinks. This is why your first payments seem to barely reduce your balance — most of it goes to interest.

The earlier you pay, the less interest you pay

Every dollar applied to early principal repayment eliminates the interest that would have been calculated on that dollar for all the remaining years. A lump-sum payment of $5,000 made early in the loan can save several thousand dollars in cumulative interest. This is the effect of reverse capitalization: less principal means less interest, so a larger share of subsequent payments attacks the principal, accelerating repayment.

Let's take a realistic case to illustrate how the calculator works. A family buys a home in Quebec City for $450,000, with a 20% down payment ($90,000) and therefore a mortgage of $360,000. The rate posted by their financial institution is 5.25% on a 5-year term, with the amortization spread over 25 years.

This result often surprises: to borrow $360,000, you end up paying nearly $646,000 — almost double. That's the reality of long amortization at a moderately high rate. The first payments contain about $1,558 in interest and only $596 in principal. Around the middle of the loan (payment 150), the two portions are roughly balanced. By the last payment, almost everything goes to principal.

What happens after the 5-year term?

In Quebec, as in the rest of Canada, the mortgage term is shorter than the amortization. After 5 years, the borrower must renew the mortgage at the prevailing market rate, which can change the monthly payment up or down. If rates rise to 6.5%, the payment would jump to about $2,350/month; if they drop to 4%, it would fall to $1,880/month.

The chosen payment frequency has a major impact on the total cost of your mortgage. The Calculix calculator lets you compare five options: monthly, bi-weekly, weekly, accelerated bi-weekly, and accelerated weekly. The distinction between regular and accelerated payments is crucial.

Bi-weekly vs accelerated bi-weekly

A regular bi-weekly payment simply divides your monthly payment into two equal halves spread over 26 payments per year (52 weeks ÷ 2). The annual total is identical to monthly mode: 12 monthly payments = 26 half-payments. No real savings result from this.

An accelerated bi-weekly payment, by contrast, takes your full monthly payment, divides it by 2, and pays it 26 times per year. You're paying the equivalent of 13 monthly payments per year instead of 12. That extra annual payment goes directly to principal and shortens the amortization by several years.

Lump-sum prepayments

Most Quebec mortgages allow annual lump-sum prepayments of 10% to 20% of the original principal without penalty. A $10,000 lump sum made early in the loan can eliminate more than $25,000 in future interest and shorten the amortization by a year and a half. Check the prepayment privileges in your contract with Desjardins, BMO, or any other lender before planning these payments.

Combining accelerated payments with annual lump sums is the most effective strategy to reduce the total cost of a mortgage. On our example, adding $5,000 per year to an accelerated bi-weekly payment can bring the total term down to under 17 years, saving over $100,000 in cumulative interest.

The Quebec mortgage market follows federal Canadian rules but also includes a few local specifics that every buyer should know before signing.

Term vs amortization

The term is the duration of the contract with your lender (usually 1, 2, 3, 4, or 5 years), while the amortization is the total time projected to fully repay the mortgage (up to 25 years for a down payment under 20%, up to 30 years for a higher down payment). At the end of each term, you must renew or refinance your mortgage.

Minimum down payment and CMHC insurance

In Canada, federal rules set the minimum down payment as follows:

• 5% on the first $500,000 of the purchase price
• 10% on the portion between $500,000 and $1,500,000
• 20% on any portion above $1,500,000 (and 20% minimum if the property costs more than $1.5M)

If your down payment is below 20%, you must obtain mortgage default insurance from the CMHC (Canada Mortgage and Housing Corporation), Sagen, or Canada Guaranty. The premium ranges from 2.8% to 4.0% of the principal, depending on the loan-to-value ratio, and is usually added to the mortgage principal (you also pay interest on it).

Quebec land transfer tax (welcome tax)

In Quebec, the buyer must pay land transfer duties, commonly called the "welcome tax". These duties are calculated on the purchase price using progressive brackets:

• 0.5% on the first $58,900
• 1.0% between $58,900 and $294,600
• 1.5% above $294,600 (up to $500,000 or $1M depending on the municipality)
• 2.0% to 3.0% on higher brackets (Montreal and Quebec City have their own scales)

For our $450,000 home in Quebec City, the welcome tax would be approximately $4,870, payable within 30 days of receiving the municipal notice (usually 3 to 6 months after purchase). This cost is not included in the amortization calculator and must be budgeted separately.

Notary and inspection fees

In Quebec, going through a notary is mandatory for any real estate transaction. Plan for $1,200 to $2,000 in notary fees, plus about $500 for a recommended pre-purchase inspection. These fees add to your purchase budget without affecting the amortization calculation.

What's the difference between a fixed and a variable rate?

A fixed rate stays the same throughout the term (e.g. 5 years at 5.25%), guaranteeing a stable payment. A variable rate fluctuates with the prime rate of Canadian banks; the payment can stay fixed (with a varying principal portion) or be adjusted at each change. Historically, the variable rate has been slightly cheaper long-term but carries the risk of increases. Discuss your risk tolerance with your mortgage broker.

Why are my first payments mostly interest?

Because interest is calculated on the remaining balance. At the start, the balance is nearly equal to the original principal, so the interest portion of each payment is very high. As the principal is paid down, the balance shrinks, less interest accrues, and more of your payment goes to principal. This is the gradual amortization effect.

Can I pay off my mortgage faster?

Yes, most Quebec lenders (Desjardins, National Bank, BMO, RBC, etc.) allow you to: (1) increase your regular payment amount by 10% to 20% per year, (2) make annual lump-sum payments of 10% to 20% of the original principal, and (3) choose accelerated bi-weekly payments. These options carry no penalty as long as you stay within the limits provided. Always check your contract before acting.

What happens at the end of the term?

You must renew or transfer your mortgage. Your lender will send you a renewal offer about 4 months before maturity. This is the ideal time to shop around and negotiate — a mortgage broker can compare several offers for you. You can also switch institutions without penalty at the end of the term. If you do nothing, your lender will automatically renew, often at a less favourable rate than you could negotiate.

Does the calculator include municipal and school taxes?

No. This calculator only computes the principal + interest portion of your mortgage. Municipal taxes (0.5% to 1.2% of the assessed value per year in Quebec), school taxes (about 0.1% of the value), home insurance, and condo fees (where applicable) must be added separately. For a $450,000 home in Quebec City, plan for an extra $400 to $500 per month for these items. Several lenders offer integrated property-tax accounts within mortgage payments to ease management.