How to Calculate Loan Interest in Canada: Simple, Compound and Amortized

Two loans with the same quoted rate can cost different amounts, because the cost depends on how the interest is calculated: whether it is charged only on the amount borrowed or also on interest already added, how often it compounds, and how each payment is split between interest and principal. This page explains the methods Canadian lenders use, the compounding rules that differ between loan types, and the payment formula behind an amortized loan, with worked examples. It is part of our personal loans and lines of credit guides.

Simple interest vs compound interest

In the formulas, P is the principal, r the annual rate as a decimal, t the time in years and n the number of compounding periods a year.

The more often interest compounds, the more it costs, though the step from monthly to daily is small. Most instalment loans don’t let interest pile up like this, because each payment covers the interest due first; the compounding frequency still sets the rate applied each period.

Canadian compounding rules by loan type

Federal student loans no longer charge interest, but the provincial part of an integrated student loan may; our guide to paying off student loans covers each province’s rules.

Converting a semi-annual mortgage rate to a monthly rate

Because Canadian fixed-rate mortgages compound twice a year but are usually paid monthly, the lender converts the quoted rate into the equivalent monthly rate:

r_monthly = (1 + r_annual ÷ 2)^1/6 − 1

Step 3 is the same loan expressed as a rate compounded monthly: it is lower than 5% only because it compounds more often, not because the loan is cheaper. The effective annual rate in step 4, the interest actually charged over a full year, is slightly above the quoted 5%. A loan quoted at 5% compounded monthly would have an effective rate higher still, which is why the compounding basis matters when comparing quotes. Our mortgage calculators apply this conversion to mortgage payments and amortization schedules.

How an amortized loan’s payment is calculated

Instalment loans, such as personal loans, car loans and mortgages, use equal payments that cover each period’s interest and repay part of the principal, so the balance reaches zero on the last payment. The payment is:

M = P × r(1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)

where M is the payment, P the amount borrowed, r the interest rate per payment period (the annual rate ÷ 12 for monthly payments on a loan compounded monthly) and n the number of payments.

Early payments are mostly interest, because interest is charged on the full balance; as the balance falls, more of each payment goes to principal. The personal loan calculator runs this formula for any amount, rate and term and shows the year-by-year split, and the car loan calculator does the same with sales tax and a trade-in.

Interest-only borrowing: lines of credit

A line of credit charges interest on the balance you carry, and the minimum payment is often only that interest, so the balance doesn’t fall unless you pay more.

The line of credit calculator shows how long a balance takes to clear at different payments. Credit card interest works the same way, but at higher rates and with a minimum payment that barely reduces the balance; how credit card interest works explains the daily calculation and the grace period.

Ways to pay less interest on a loan