How compound growth works
Compound growth means earning returns on your past returns, not just on what you put in. Here is how it works, with simple examples and the rule of 72.
Compound growth is when your returns start earning returns of their own. Over time, this can make money grow faster than it would if only the original amount earned a return. Time is the biggest factor.
Simple vs compound growth
Simple growth pays a return on the original amount only.
Compound growth pays a return on the original amount plus all the returns already added.
Here is the difference with $1,000 growing at 5% a year.
With simple growth, you earn $50 every year. After 10 years, you have $1,500.
With compound growth:
- After year 1, you have $1,050.
- In year 2, you earn 5% on $1,050, which is $52.50. You now have $1,102.50.
- In year 3, you earn 5% on $1,102.50, and so on.
After 10 years, you have about $1,629. The extra $129 comes from returns earned on earlier returns.
These numbers are only an illustration. Real investments do not grow at a steady rate every year.
Why time matters so much
The gap between simple and compound growth starts small and grows each year.
Using the same $1,000 at 5% a year:
- After 10 years, compound growth gives about $1,629.
- After 20 years, about $2,653.
- After 30 years, about $4,322.
With simple growth, 30 years would give $2,500. The longer the money compounds, the wider the gap.
This is why people often say that starting earlier matters more than starting with a large amount.
The rule of 72
The rule of 72 is a quick way to estimate how long it takes money to double.
Divide 72 by the yearly growth rate. The answer is roughly the number of years needed.
- At 4% a year, money doubles in about 18 years.
- At 6% a year, about 12 years.
- At 8% a year, about 9 years.
It is an estimate, not an exact figure, and it assumes a steady rate.
Where compounding shows up in investing
Reinvested dividends. When you use dividends to buy more shares, those new shares can pay dividends too. This is a direct form of compounding.
Rising prices on a growing base. If an investment grows, the next year's change applies to the larger amount.
Interest on interest. Savings accounts and bonds that let interest build up use compounding. See what a bond is.
Tax-sheltered accounts. Accounts that shelter growth from yearly tax let more of the returns stay invested. Examples include the TFSA and RRSP in Canada and the 401(k) and IRA in the US.
Compounding works against you too
The same math applies to costs and debt.
Fees. A yearly fee takes a percentage of your money every year. The amount lost to fees also stops compounding for you. Small differences in fees can add up to large differences over decades. See mutual funds vs ETFs.
Debt. Credit card balances and loans that charge interest on unpaid interest grow in the same way.
Inflation. Rising prices compound too. Over many years, inflation can greatly reduce what a fixed amount of money can buy.
Losses and uneven returns
Real returns go up and down. A loss hurts compounding because it shrinks the base that future growth applies to.
A 50% loss needs a 100% gain to get back to where you started. If $1,000 falls to $500, it must double to return to $1,000.
This is one reason why the average yearly return can look better than what an investor actually earned. Uneven returns compound to less than steady returns with the same average. You can read more in what volatility means.
Adding money over time
Compound growth is not only about a single starting amount. Adding money regularly gives each new contribution its own time to grow. Many people do this on a fixed schedule. See what dollar-cost averaging is.
The short version
- Compound growth means earning returns on past returns.
- The effect is small at first and grows larger over time.
- The rule of 72 estimates how long it takes money to double.
- Fees, debt and inflation compound against you in the same way.
- Losses shrink the base, so uneven returns compound to less.
This is general information, not investment advice.
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