How Compound Growth Works | How Do Stocks Work?

Compound growth means earning returns on your past returns, not just on the money you originally put in. Because each year’s gain is added to the base that next year’s gain is calculated on, the dollar amount of growth gets larger over time even if the percentage stays the same.

In short: with compounding, money grows by a percentage of an ever-larger balance. The formula is ending value = starting value × (1 + r)ⁿ, where r is the yearly return and n is the number of years. Time matters as much as the rate, and fees, taxes and inflation compound too, in the other direction.

Simple growth versus compound growth

Start with $10,000 earning 7% a year.

With simple growth, you earn 7% of the original $10,000 every year: $700 a year, forever. After 30 years you have $10,000 + (30 × $700) = $31,000.

With compound growth, each year’s 7% is calculated on the new, larger balance:

Year 1: $10,000 × 1.07 = $10,700 (gain of $700)
Year 2: $10,700 × 1.07 = $11,449 (gain of $749)
Year 3: $11,449 × 1.07 = $12,250 (gain of $801)

The percentage never changes. The dollar gain does, because the base keeps getting bigger.

The curve bends upward

Here is the same $10,000 at 7% a year over longer periods, with no additions and no withdrawals:

Years	Ending value	Gain in that decade
0	$10,000
10	$19,672	$9,672
20	$38,697	$19,025
30	$76,123	$37,426
40	$149,745	$73,622

The fourth decade adds more than the first three decades combined. That is the defining feature of compounding: most of the growth arrives late. It is also why the starting date matters so much. Someone who stops at 30 years ends with about half of what someone who stays to 40 years has.

The rule of 72

A quick way to estimate doubling time: divide 72 by the annual percentage return.

At 7%, 72 ÷ 7 ≈ 10.3 years to double. The exact answer, using logarithms, is 10.24 years.
At 10%, 72 ÷ 10 = 7.2 years. Exact: 7.27 years.
At 2.5%, 72 ÷ 2.5 = 28.8 years.

The rule is an approximation that works best for rates between roughly 6% and 10%. It also works for anything that compounds, including inflation and fees. At 3% inflation, prices double in about 24 years. Run it backwards and a 2% annual fee, on its own, takes about half of a balance’s value in roughly 36 years (0.98 multiplied by itself 36 times is about 0.48).

How often it compounds

Interest on savings accounts and bonds is often quoted as an annual rate but credited more frequently. The more often returns are added to the balance, the slightly faster it grows, because each credit starts earning sooner.

7% compounded once a year is exactly 7% a year.
7% compounded monthly is (1 + 0.07 ÷ 12)¹² - 1 = 7.23% a year. Banks call this the effective annual rate, or annual percentage yield in the US.
7% compounded daily is about 7.25% a year.

Over 30 years, $10,000 at 7% compounded annually grows to $76,123; at 7% compounded monthly, it grows to about $81,165. The frequency matters, but much less than the rate and the number of years.

Stocks do not pay a quoted rate at all. Their return comes from price changes and dividends, and the compounding happens because gains stay invested and dividends can be reinvested to buy more shares. A stock return quoted “per year” over a long period is almost always a compound annual rate, described in the section on averages below.

Regular contributions

Most people do not invest one lump sum and walk away. They add money from each paycheque, often through a 401(k), RRSP, or TFSA (see US retirement accounts explained and Canadian registered accounts explained).

Suppose you invest $6,000 at the start of each year (about $500 a month) and earn 7% a year.

Plan	Years	Total contributed	Ending value
Start now	30	$180,000	$606,438
Start 10 years later	20	$120,000	$263,191

The later starter contributes two-thirds as much money but ends with well under half the balance. The missing decade is not just $60,000 of contributions; it is the decade during which the early contributions would have been compounding at the largest balances.

These numbers assume a smooth 7% every year, which real markets never deliver. The pattern holds even with bumpy returns, but the ending value will be different.

Nominal returns versus real returns

A nominal return is the percentage change in dollars. A real return is the change in purchasing power, after inflation.

The exact relationship is:

(1 + real return) = (1 + nominal return) ÷ (1 + inflation)

With a 7% nominal return and 2.5% inflation:

1.07 ÷ 1.025 = 1.0439, so the real return is about 4.39%.

The shortcut “7% minus 2.5% = 4.5%” is close but slightly high. Over long periods the difference matters.

What that does to the table

Our $10,000 growing for 30 years reaches $76,123 in nominal dollars. In today’s purchasing power, at a 4.39% real return, it is worth about $36,300. Both numbers are correct. One tells you how many dollars you will have; the other tells you roughly what they will buy.

For reference, both the US Federal Reserve and the Bank of Canada target inflation of 2% a year over time, though actual inflation has been well above that in some years.

What historical returns looked like

According to the SPIVA U.S. Year-End 2025 Scorecard from S&P Dow Jones Indices, the S&P 500 returned an annualized 11.00% over the 20 years ending December 31, 2025, including dividends. That is a nominal figure, before inflation, taxes, and fund fees, and it covers one specific stretch of history that included both the 2008 financial crisis and a strong recovery. It is not a forecast. A different 20-year window can look very different, which is covered in bull and bear markets.

Average returns versus compound returns

There is a trap in the word “average.” Suppose an investment gains 50% one year and loses 50% the next. The arithmetic average return is (50% - 50%) ÷ 2 = 0%. But the money:

$10,000 × 1.50 × 0.50 = $7,500

You lost 25%. The compound annual growth rate (CAGR), which is what actually determines your wealth, is negative.

A milder example: +20% then -10%. The arithmetic average is 5% a year. The compound result is 1.20 × 0.90 = 1.08, an 8% total gain over two years, or about 3.92% a year. Volatility pulls the compound return below the simple average. The bigger the swings, the bigger the gap. When someone quotes an “average return,” it is worth asking which kind.

Compounding works against you too

Fees compound. A 1% annual fee does not cost you 1% of your money. Over decades it costs you a far larger share of your ending balance, because the fee is taken from the growing balance every year and the money taken never compounds for you. The full arithmetic is in how investment fees work.
Taxes compound. Paying tax on gains each year shrinks the base that keeps growing. This is the main reason tax-sheltered accounts matter.
Debt compounds. Credit card interest at 20% doubles a balance in about 3.6 years by the rule of 72.
Inflation compounds. Cash earning nothing loses purchasing power at the rate of inflation, every year.

What can go wrong

Returns are not smooth. Real markets go up and down, sometimes for years. A worked example with a constant 7% hides the experience of watching a balance fall 30% or more.
Sequence matters when money moves. If you are adding or withdrawing money, the order of good and bad years changes your result. A big decline just before retirement, when the balance is largest, hurts more than the same decline early on.
Interrupting the process is expensive. Because most growth comes late, selling in a downturn or stopping contributions for years removes the part of the curve that does the most work. See investor behavior mistakes.
Assumed rates can be wrong. A plan built on 10% a year that delivers 5% ends with less than half the money after 30 years. Planning with conservative rates is safer than planning with optimistic ones.

The short version

Compounding means growth on growth, so the dollar gains get bigger every year and most of the result arrives late. The rule of 72 estimates doubling time. Starting earlier matters more than most people expect. Real returns, after inflation, are what measure purchasing power. And fees, taxes, and debt compound with exactly the same force, which is why small percentages matter over long periods.