What is compound interest?
With simple growth, you earn a return only on the money you put in. With compounding, each year’s return is added to the balance and earns returns of its own. The drawing at the top of the page shows a hypothetical $10,000 growing 7% a year: simple growth adds $700 every year and reaches $31,000 after 30 years; compounded, the same 7% reaches about $76,100. The gap is growth earned on earlier growth.
For stock investors, compounding happens when you reinvest: dividends used to buy more shares, gains left invested instead of spent; dividend investing covers the dividend side. One note for Sharia-conscious investors: compounding here means reinvested returns from owning assets, such as price gains and dividends, while interest-bearing products raise questions of their own, covered in halal stock investing.
- Compound growth
- Growth in which each period’s return is added to the balance, so later returns are earned on a larger base.
- Simple growth
- Growth earned only on the original amount; returns that are taken out are not reinvested.
- Reinvestment
- Putting returns, such as dividends, back into the investment instead of spending them.
The compound interest formula, with an example
Future value = present value × (1 + r)^n, where r is the yearly rate and n the number of years. Hypothetical: $10,000 at 7% for 10 years is 10,000 × 1.07^10 ≈ $19,700. After 20 years it is about $38,700, after 30 about $76,100. The first decade adds about $9,700; the third adds about $37,400 at the same rate, because the base is bigger.
When returns are credited more often than once a year, the formula uses the rate per period and the number of periods; that detail matters far less than the rate and the time. Stock returns are not credited at all: they arrive unevenly, some years are negative, and a fall early on shrinks the base everything later grows from, as stock market crashes shows. Use the formula to see the shape, not as a promise.
The rule of 72: how long does it take to double your money?
Divide 72 by the yearly rate in percent to estimate how many years it takes to double: about 18 years at 4%, 12 at 6%, 9 at 8% and 6 at 12%. At a hypothetical 8%, $10,000 would become about $20,000 after 9 years, $40,000 after 18 and $80,000 after 27, as the drawing below shows.
It is an approximation, closest for rates between about 6% and 10%. It works for anything that compounds, costs included: inflation of 3% a year halves the buying power of idle cash in about 24 years.
Time vs rate: why starting early matters
In the formula, time is the exponent. The grid below shows a hypothetical $10,000 at 4%, 6% and 8% after 10, 20 and 30 years. At 6% for 30 years it ends near $57,400; at 8% for only 20 years, near $46,600. Ten more years beat two more points of return.
That is why many long-term investors start with small sums and keep adding rather than waiting to start big. Regular contributions, as in dollar-cost averaging, give each deposit its own years to compound, and a broad index fund keeps costs low while they do. Keep in mind that a higher expected return usually comes with higher risk.
How fees and taxes slow compounding
Costs compound too, in the other direction: a yearly fee or tax comes off every year’s return, and so does the growth that money would have earned. Hypothetical: $10,000 for 30 years at 7% before costs ends near $76,100. Net of 0.5 points a year, about $66,100; net of 1 point, about $57,400; net of 2 points, about $43,200. One point a year left about a quarter less at the end.
Fund expense ratios are the classic case; what is an ETF shows where to find them. Taxes work the same way: for non-US investors, US dividends face a 30% withholding by default unless a tax treaty lowers it, so a hypothetical 2% dividend yield reinvests as 1.4%; see how dividends work. Frequent trading adds commissions and spreads on top, one reason trading often and compounding pull in opposite directions.