Compound Interest Explained: How Money Grows Over Time

What Is Compound Interest?

Compound interest is interest calculated on both the original amount of money (the principal) and interest accumulated from earlier periods.

When that interest is added to the balance, it becomes part of the amount on which future interest is calculated. This is commonly called earning "interest on interest."

How Compound Interest Works

Suppose you invest $10,000 at an annual interest rate of 8%, with all earned interest remaining invested. Each year, the interest is added to your balance, and the following year's interest is calculated on that new amount.

Multiplying by 1.08 accounts for both your existing balance (1.00) and the additional 8% interest (0.08).

Year 1

$10,000 × 1.08 = $10,800

You earn $800 in interest.

Year 2

$10,800 × 1.08 = $11,664

You earn $864 in interest, including $64 earned on the previous year's $800.

Year 3

$11,664 × 1.08 = $12,597.12

You earn $933.12 in interest.

The amount of interest earned grows each year because the same 8% rate is applied to an increasingly large balance. This pattern continues for as long as the money remains invested and earns a positive return.

What $10,000 Becomes at 8% a Year

Assumptions: $10,000 invested once, a constant 8% effective annual return, annual compounding, and no contributions, withdrawals, taxes, or fees. Values are rounded to the nearest dollar.

The first 20 years add $36,610, while the ten years from year 30 to year 40 add another $116,618 because the same 8% return is being earned on an increasingly large balance.

Simple Interest vs. Compound Interest

Let's hold the deposit, the interest rate, and the time period constant: $10,000 at 8% for 30 years.

With simple interest, interest is calculated only on the original $10,000. That is $10,000 × 8% = $800 per year, or $800 × 30 = $24,000 over 30 years, for a final amount of $34,000 once the original deposit is added back.

With compound interest, each year's earnings are added to the balance and earn interest in later years. After 30 years:

$10,000 × (1.08)³⁰ = $100,627

The $66,627 difference comes entirely from leaving the earnings invested.

The Compound Interest Formula

A = P(1 + r/n)^nt

Where:

• A = final amount
• P = principal, or starting amount
• r = nominal annual interest rate, expressed as a decimal
• n = number of times interest compounds per year
• t = time in years

For annual compounding, n = 1 and the formula simplifies to A = P(1 + r)^t. Using our example, A = $10,000 × (1.08)³⁰ = $100,627.

Time sits in the exponent. Each additional year multiplies the balance by the growth factor again rather than adding a fixed amount, which is why the growth curve bends upward instead of rising in a straight line.

How Often Does Interest Compound?

It depends on the financial product. Interest can compound annually, semi-annually, quarterly, monthly, or daily. Canadian fixed-rate mortgages are quoted with semi-annual compounding, while many savings accounts credit interest monthly. At the same nominal annual rate, more frequent compounding produces a higher effective annual return. For $10,000 at a nominal 8%, one year produces $10,800 with annual compounding and approximately $10,830 with monthly compounding. Over 30 years, the gap between annual and monthly compounding grows to $8,730:

The annual row matches our main example, where 8% is an effective annual return. Compounded monthly, a nominal 8% works out to an effective annual return of approximately 8.30%. When comparing financial products, check whether the quoted rate is nominal or effective. With no deposits or withdrawals, two products with the same effective annual rate grow identically over complete years, regardless of how frequently interest is credited.

Why Time Matters

Early growth can feel slow because the gains are relatively small. In our example, the first ten years add $11,589, while years 21 through 30 add $54,017, more than four times as much and approximately 54% of the final balance. Starting earlier lets those larger later gains accumulate: after 25 years the original $10,000 would be worth $68,485, and after 30 years it would be worth $100,627, so five additional years add $32,142 without any further contributions.

The same principle applies to people making regular contributions. Someone who starts saving earlier generally needs smaller contributions to reach the same future target, assuming identical positive returns. The article Why Starting to Invest Early Matters and the Cost of Waiting to Invest Calculator explore this comparison further.

Why Small Differences in Return Matter

Two investors each start with $10,000 and stay invested for 30 years, one earning 7% annually and the other 8%. After the first year the difference is only $100. After 30 years the results are considerably further apart:

A one-percentage-point difference in annual return produces an additional $24,504, approximately 24% of the final balance in the 8% scenario. This is why investment costs deserve attention. Management fees and other ongoing expenses reduce the returns investors keep, and a 1% annual fee costs the dollars paid plus the growth those dollars could otherwise have earned. Over several decades, that lost growth can substantially increase the total cost. The Cost of a 1% Annual Fee calculator shows the effect using your own investment balance and time horizon.

The Rule of 72

The Rule of 72 provides a quick way to estimate how long an investment takes to double: divide 72 by the annual rate of return, expressed as a percentage. At 8%, 72 ÷ 8 = 9 years. The mathematically exact doubling time is approximately 9.006 years, and an initial $10,000 would be worth approximately $19,990 after nine years. The rule is an approximation, but it works particularly well for annual rates between about 4% and 12%.

Does Compound Interest Apply to Stocks?

In effect, yes, although stocks do not pay interest, so the more precise term is compound growth. Suppose a stock rises 10% from $100 to $110, then rises another 10% the following year to reach $121. The second year's $11 gain exceeds the first year's $10 gain because it was earned on a higher starting value. Reinvested dividends work similarly: they purchase additional shares, which can participate in future price appreciation and potentially generate further dividends.

Investment returns are not guaranteed, and they rarely arrive at the same rate every year.

A portfolio that gains 20% and then loses 20% goes from $100 to $120 to $96, a 4% loss overall. The two changes don't cancel each other out because the second percentage applies to a different starting balance. Compounding describes how successive returns affect an investment, and those returns can be positive or negative. The smooth growth curves in this article illustrate the mathematics rather than predict how markets will perform.

With no contributions or withdrawals, changing the order of annual returns does not change the final balance. However, the sequence of returns matters during accumulation when contributions are being made, and when investments are being sold to fund withdrawals. Our Sequence of Returns Risk article explains this in greater detail.

Compounding Also Works Against You

The same mathematical principles apply to inflation and certain types of debt.

Inflation

Inflation causes prices to rise over time, with each increase building on earlier increases. At a constant 3% inflation rate, something costing $100 today would cost approximately $243 in 30 years. The purchasing-power calculation works in reverse as well: $100 received 30 years from now would buy approximately what $41 buys today. An investment portfolio worth $100,000 several decades from now will therefore have less purchasing power than $100,000 has today, assuming prices continue to rise.

Milk offers a real-world illustration. Statistics Canada's historical tables list milk at approximately 11.8 cents per quart in 1926, equivalent to about 12.4 cents per litre using the 0.95-litre quart convention identified in its historical price comparisons. In August 2026, national average retail prices were about $1.75 per litre for a 4-litre jug and $2.75 per litre for a 2-litre carton. Compounding the historical price at 3% annually for 100 years produces approximately $2.40. An individual product's price does not follow overall inflation exactly, and Canada's actual CPI did not rise at precisely 3% a year over the century, so the example illustrates the arithmetic rather than measuring inflation.

Sources: Statistics Canada, Canada Year Book, archived historical table (1926 milk prices); Statistics Canada, Prices Over the Decades (0.95-litre quart convention); Statistics Canada, Table 18-10-0245-02, Monthly Average Retail Prices for Selected Products: Food. The 1926 table records prices per quart without specifying the quart's volume. The conversion above applies the 0.95-litre convention used in Statistics Canada's later historical comparison.

The article Inflation: The Math That Makes Future Money Smaller explores the effect of rising prices on purchasing power in greater detail. The Inflation Time Machine (Then → Now) shows these effects using historical consumer price data from multiple countries.

Debt

When unpaid interest is added to an outstanding debt balance, future interest can be charged on that larger amount, so the debt can grow increasingly quickly if payments are insufficient to cover the interest. A typical amortizing loan works differently: each regular payment covers the interest owing and reduces the principal, so the interest charged generally falls as the balance decreases.

Taxes and Registered Accounts

The examples above ignore taxes, which affect how much money remains available to compound. In Canada, growth inside a TFSA is generally tax-free and an RRSP defers tax until withdrawal, while non-registered investments are taxed differently depending on whether the income is interest, dividends, or capital gains. For more detail, see What Is a TFSA?, What Is an RRSP?, and Capital Gains vs. Dividends vs. Interest Tax in Canada.

Run the Numbers Yourself

The Simple Investment Calculator lets you enter a starting balance, contribution amount, investment horizon, and assumed annual return to estimate how an investment could grow with regular contributions. For a static reference showing how $1 grows at different annual rates over periods of up to 50 years, see the Compound Interest Tables.

The Takeaway

Compound growth depends on four things: how much money is invested, how long it remains invested, the returns it earns, and how much of those returns is retained after costs and taxes. The same arithmetic helps explain inflation, borrowing costs, and why seemingly small differences in investment returns can become significant over several decades.

It also explains our opening example. The same $10,000 investment earning the same 8% generated $800 in its first year and approximately $7,454 in its thirtieth year. The only thing that changed was the amount of money earning that return.

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