Compound interest is interest earned on both the original principal and on the interest already earned. Each year’s interest joins the principal, so next year’s interest is calculated on a larger base. The formula is A = P(1 + r/n)^(n×t), where P is principal, r is annual rate, n is compounding periods per year, and t is years. At a 7% return, money roughly doubles every 10.3 years (the “Rule of 72”).
Quick answer: Compound interest earns interest on interest. $10,000 at 7% over 30 years grows to about $76,000 with annual compounding — the original is only $10,000, the other $66,000 is compounding.
What this means: Time matters more than rate. Starting at 25 instead of 35 with the same monthly contributions roughly doubles your retirement balance, because the early dollars get 10 extra compounding years.
What to do next: See compound interest on your specific principal, rate, and timeline. Run the compound calculator →
The compound interest formula
A = P (1 + r/n)n × t
Where:
- A = future value (the answer)
- P = principal (the starting amount)
- r = annual interest rate (as a decimal: 7% = 0.07)
- n = number of compounding periods per year (12 for monthly, 4 for quarterly, 365 for daily, 2 for semi-annual)
- t = time in years
Example: $10,000 at 7% annual, monthly compounding (n=12), 20 years:
A = 10,000 × (1 + 0.07/12)12 × 20 = 10,000 × (1.005833)240 = 10,000 × 4.0387 = $40,387
The Rule of 72 (mental shortcut)
To estimate how long money takes to double at a given rate:
Years to double = 72 / annual rate (in percent)
| Annual rate | Years to double |
|---|---|
| 3% | 24 years |
| 5% | 14.4 years |
| 6% | 12 years |
| 7% | 10.3 years |
| 8% | 9 years |
| 10% | 7.2 years |
| 12% | 6 years |
The Rule of 72 is accurate to about 1-2% for rates between 4% and 12%. For credit card APRs (19-24%), it underestimates — debt at 24% doubles in about 3.2 years.
Why time matters more than amount
| Investor | Starts at | Monthly contribution | Stops at | Balance at 65 (7% return) |
|---|---|---|---|---|
| Early Edith | Age 25 | $300 | Age 35 (stops contributing) | ~$430,000 |
| Late Larry | Age 35 | $300 | Age 65 (contributes 30 years) | ~$367,000 |
Edith contributed only $36,000 over 10 years. Larry contributed $108,000 over 30 years. Edith finished with more, because her early contributions had an extra decade to compound.
How often interest compounds
The more frequently interest compounds, the higher the effective annual return. For practical Canadian investments:
- Most Canadian savings accounts: Daily compounded, monthly paid
- Most Canadian mortgages: Semi-annual compounding by law (Interest Act, Section 6)
- GICs: Annual, semi-annual, or at maturity (varies)
- Bonds: Semi-annual (Government of Canada bonds)
- Most ETFs / mutual funds: Continuous (returns accumulate intra-day; distributions paid quarterly)
Practical impact: at 5% annual rate, $10,000 over 20 years grows to:
- Annual compounding: $26,533
- Semi-annual: $26,851
- Monthly: $27,126
- Daily: $27,181
The difference between annual and daily is about 2.4%. Real, but small relative to the choice of rate.
Compounding plus monthly contributions
The compound interest formula above handles a one-time lump sum. With regular monthly contributions, use:
A = P (1+r/n)nt + PMT × [((1+r/n)nt − 1) / (r/n)]
This is what a TFSA or RRSP calculator runs in the background. Example: $5,000 starting balance, $400 monthly contribution, 7% annual return, monthly compounding, 30 years:
| Initial $5,000 grows to | ~$40,640 |
| Monthly contributions grow to | ~$486,720 |
| Total at year 30 | ~$527,360 |
| Out of which, contributions | $149,000 |
| Out of which, compound growth | $378,360 |
72% of the ending balance is compound growth, not contributions.
When compound interest works against you
Debt compounds too. Canadian credit card APRs of 19.99-24.99% compound daily. Carrying a $5,000 balance with only minimum payments:
- At 21% APR and $100 minimum payments: 79 months to pay off, $5,440 in interest paid
- At 21% APR and $200 monthly payments: 32 months, $1,716 in interest
- At 21% APR and $400 monthly payments: 14 months, $698 in interest
Compound interest on debt is the most common reason people stay financially stuck. Paying down credit card balances is mathematically equivalent to earning a 21%+ return guaranteed and tax-free — no investment matches it.
Real-world Canadian numbers to anchor expectations
- HISA / savings account: 3-4.5% (taxable in non-registered, tax-free in TFSA)
- GICs: 4-5% (taxable in non-registered)
- Diversified equity portfolio long-term: 6-8% nominal, 4-6% real (after inflation)
- S&P 500 historical (1928-2024): ~10% nominal, ~7% real
- TSX historical (1956-2024): ~9% nominal, ~5-6% real
- Inflation in Canada (long-term): ~2-3%
For Canadian retirement modelling, 6% nominal (4% real) is a defensible middle-of-the-road return for a balanced portfolio.
Frequently asked questions
- What is the compound interest formula?
- A = P (1 + r/n)^(n × t), where P is principal, r is annual rate as a decimal, n is compounding periods per year, and t is years.
- What is the Rule of 72?
- Years to double money = 72 divided by the annual percentage rate. At 7%, money doubles in about 10.3 years; at 12% it doubles in 6 years.
- How does compounding frequency affect returns?
- More frequent compounding produces slightly higher returns. At 5% over 20 years, annual compounding grows $10,000 to $26,533 while daily compounding grows it to $27,181 — a 2.4% difference.
- Why does starting early matter so much?
- Early contributions get many more compounding years. A $300/month investor from age 25-35 can finish with more than a $300/month investor from age 35-65 because of those 10 extra compounding decades.
- Do Canadian mortgages use monthly compounding?
- No. By federal law (Interest Act, Section 6), Canadian mortgage rates are quoted with semi-annual compounding. This makes Canadian mortgage payments lower than they would be with monthly compounding at the same nominal rate.
- How does compound interest affect credit card debt?
- Credit card debt at 21% APR compounded daily can take 79 months to pay off with minimum payments only, costing over $5,000 in interest on a $5,000 balance.
- What is a realistic long-term return on Canadian investments?
- A diversified equity portfolio historically returns 6-8% nominal annually (about 4-6% after inflation). The TSX has returned about 9% nominal and 5-6% real since 1956.