Compound Interest, Explained: Five Worked Examples in Canadian Dollars

Compound interest is the math of interest charged on previously earned interest. On the savings side: $5,000 left alone in a TFSA at 6% for 30 years grows to roughly $28,700, while the same money earning simple interest would reach only about $14,000. On the borrowing side: $10,000 on a credit card at 22% APR adds about $2,200 in interest in the first year if nothing is paid down, and minimum payments alone keep the balance outstanding for nearly three decades. The same formula drives both. The levers that change the outcome are rate, time, compounding frequency, and how often you add or withdraw.

Most explanations of compound interest stop at the formula. That makes the concept memorable and the dollar figures abstract. This article does the opposite: five worked examples in Canadian dollars, each with the input numbers, the result, and the one or two levers most worth pulling. The examples cover both sides of the ledger because most Canadian households face both at the same time.

Sources are anchored to the Bank of Canada, the Canada Revenue Agency, the Financial Consumer Agency of Canada (FCAC), the Office of the Superintendent of Financial Institutions (OSFI), and Statistics Canada's Survey of Financial Security. Where US data is cited (for example Federal Reserve G.19 credit card statistics), the comparable Canadian source is named.

The Mechanics: What "Compounding" Actually Does

The formal expression is the standard compound interest formula: final amount equals principal multiplied by one plus the rate divided by the number of compounding periods per year, all raised to the power of the periods per year times the number of years. In notation: A = P(1 + r/n)^(nt). What that produces in practice is a curve, not a line. A line is what simple interest produces, where you earn or pay the same dollar amount every year on the original principal. A curve is what happens when each period's interest gets added to the base and then earns its own interest the next period. The curve looks gentle for the first decade and steep after the second.

This shape is why time matters more than rate for most households. A 7% return for 30 years beats a 9% return for 20 years on the same starting capital. The Bank of Canada has published versions of this point in financial literacy materials going back to 2018, and the Investor Education Fund (now the Ontario Securities Commission's GetSmarterAboutMoney) makes the same case using TFSA examples.

Example 1: $5,000 in a TFSA at 6% for 30 Years

The numbers come straight from the standard formula. At year ten, the $5,000 is worth roughly $8,955. At year twenty, it is worth roughly $16,036. At year thirty, it is worth roughly $28,717. Notice the gap between year ten and twenty is about $7,000, but the gap between year twenty and thirty is about $12,700 — same number of years, much larger absolute gain. That asymmetry is the curve doing its work. The 6% rate is conservative for a long-horizon Canadian equity portfolio: historical S&P/TSX Composite total return averages over rolling 25-year periods, measured by the Canadian Institute of Actuaries, sit in the 7% to 9% nominal range before fees.

Two levers change this outcome the most. Starting earlier is the biggest: every five years of extra runway adds roughly $7,000 to $12,000 in the back half. Adding contributions is the second: a $5,000 lump becomes a different curve entirely with even modest annual top-ups. The Unburden compound interest calculator runs both scenarios side by side.

Example 2: $10,000 in a Credit Card at 22% APR

This is the same compounding formula working in reverse. Each day, the issuer calculates interest on the average daily balance at 22%/365, adds it to the balance, and the next day's interest is calculated on the slightly larger figure. The monthly cycle then assesses the accumulated interest and bills it. Minimum payments are typically structured at 2% to 3% of the outstanding balance, which on $10,000 is roughly $250. Of that $250, about $183 covers monthly interest accrual. Only $67 reduces principal. At that rate, the balance does not meaningfully fall for years.

The lever that matters most here is not the rate (changing cards rarely cuts more than three to five percentage points) but the monthly payment above the minimum. Adding $200 above the minimum clears $10,000 in about 39 months. Adding $400 clears it in about 24 months. Our full walkthrough lives in Got $10,000 in Credit Card Debt? Here's the Plan, which uses the same FCAC and Federal Reserve data.

Example 3: $300 a Month into an RRSP at 7% for 25 Years

Recurring contributions change the shape of the curve. Instead of one principal earning compounded interest, each $300 contribution starts its own compounding clock from its deposit date. The earliest dollars (month one) compound for 25 years; the latest dollars (month 300) compound only briefly. The total is the sum of all these mini-curves, which is why the formula for the future value of an annuity replaces the lump-sum formula in this case.

The two largest levers are the contribution amount and the rate of return. Doubling the contribution to $600 per month at the same 7% return produces roughly $487,200 after 25 years — a clean doubling, as you would expect. Holding the contribution steady and raising the return to 8% produces about $284,600 — a $41,000 improvement for one percentage point over 25 years. Most Canadian households have more control over the contribution amount than the rate of return; the OSC's GetSmarterAboutMoney consistently makes this point.

Example 4: A $25,000 Student Loan at Prime Plus 2.5%

Canada Student Loans compound monthly, which is less aggressive than credit card daily compounding but more aggressive than the semi-annual compounding required on Canadian fixed-rate mortgages. The monthly interest accrual on $25,000 at 8.45% is roughly $176. A standard 10-year payment of about $309 puts $133 toward principal in month one — a meaningful reduction, but slow. Provincial student loan portions (Ontario Student Loans through OSAP, Alberta Student Aid, etc.) have varied rates; Ontario's portion has been interest-free for residents since 2023, which materially changes the consolidated math for Ontario borrowers.

Two levers stand out. Lump-sum prepayments during the six-month grace period (where interest accrues but no payment is due) reduce the balance the amortization runs on. Switching to weekly payments effectively makes 52 weekly payments per year (the equivalent of 13 monthly payments), which trims a few months off the term. Our deeper walkthrough is in Student Loan Payoff Strategies in Canada.

Example 5: The Cost of Waiting Five Years to Start

This is the example that makes the curve real. The five years of "lost" contributions amount to $12,000 ($200 × 60 months). The $161,000 gap is more than 13 times the missed contributions, which feels disproportionate until you realize the missed dollars are the ones that would have compounded the longest. The first $200 contributed at age 25 would have compounded for 40 years; the $200 from year six only gets 35 years. Each year of delay specifically removes the most valuable years of compounding from the back end of the curve.

The reverse is also true on the debt side. Letting a $10,000 credit card balance sit for five years on minimum payments grows the total interest paid over the eventual payoff period by more than 80%, because the early years are when the balance — and therefore the interest accrual — is largest. Time is the lever that pays back fastest in both directions.

Why Frequency Matters: Monthly vs Daily Compounding

The Rule of 78, the Actuarial Method, and the simple-interest method are three other interest-calculation conventions still used on some Canadian installment loans and rent-to-own products. The Consumer Protection Act in Ontario and equivalent legislation in other provinces requires the effective annual rate to be disclosed regardless of which method is used, which makes apples-to-apples comparison possible if you read the fine print. The Bank of Canada publishes a consumer guide that walks through each convention.

For most Canadian households, the practical takeaway is that compounding frequency is a tiebreaker, not a deciding factor. The rate and the payment matter more by an order of magnitude. The only place frequency materially changes outcomes is on very long-horizon investment products with continuous compounding, which in practice means specific institutional vehicles, not retail TFSAs or RRSPs.

When Compound Interest Works For You vs Against You

The clean version of this trade-off is: compare your highest-APR debt rate to your expected long-term investment return. On a 22% APR credit card, no diversified portfolio reliably matches 22% net of fees and tax — so paying that debt down is the mathematically dominant move. On a 4% mortgage held by someone in a high TFSA contribution position, a 7% expected equity return makes contributing to the TFSA the dominant move. The break-even sits somewhere between 6% and 9% APR for most Canadians, depending on tax situation and risk tolerance.

The deeper trap is that compound interest on debt is certain (the issuer charges it whether you can afford it or not) while compound returns on investments are expected, not certain. That asymmetry is why most financial-literacy materials from the FCAC, OSC, and Canadian Bankers Association lean toward paying down high-interest debt before maximizing investment contributions, even when the expected return looks higher on paper. Our full breakdown of the question lives in Pay Off Debt or Invest? The Math in Canadian Dollars.

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