Compound interest is interest that is earned on the money you have saved and on the interest that money has already earned. It is the reason a small amount saved early can grow into a large amount, and it is the reason debt that is not paid off can grow quickly too. This guide explains how it works, shows the arithmetic step by step, and draws out the practical lessons for saving and investing.
Simple interest and compound interest
With simple interest, you earn a fixed amount each year, calculated on the original sum only. If you deposit 1,000 at 5 percent simple interest, you earn 50 each year. After ten years you have 1,500.
With compound interest, the interest is added to the balance, and the next year's interest is calculated on the larger figure. The same 1,000 at 5 percent compounded yearly earns 50 in the first year, then 52.50 in the second, because the second year's interest is calculated on 1,050. The gap grows every year.
The difference looks small at first and becomes large over time. That is why the arithmetic matters.
The formula
The standard formula is:
Future value = Principal × (1 + rate) to the power of years
Here the rate is written as a decimal, so 5 percent is 0.05, and "1 + rate" is 1.05. The power is the number of compounding periods. If interest is added yearly, that is the number of years. If it is added monthly, you divide the annual rate by 12 and multiply the number of years by 12.
A worked example
Take 10,000 invested at 8 percent a year, compounded yearly, for ten years.
The future value is 10,000 × (1.08) to the power of 10. The value of 1.08 to the power of 10 is about 2.159, so the result is about 21,590. The money has more than doubled, and the interest earned is about 11,590.
| Year | Balance at start | Interest at 8% | Balance at end |
|---|---|---|---|
| 1 | 10,000 | 800 | 10,800 |
| 2 | 10,800 | 864 | 11,664 |
| 3 | 11,664 | 933 | 12,597 |
| 5 | 13,605 | 1,088 | 14,693 |
| 10 | 19,990 | 1,599 | 21,589 |
The interest in each year is larger than the one before, because it is calculated on a bigger balance. That is the whole mechanism.
Time matters more than the rate
Two people save the same amount at the same rate, but one starts ten years earlier. The earlier starter has far more money at the end, even though the total they put in is the same.
Consider 1,000 invested at 7 percent. Left for 10 years, it grows to about 1,967. Left for 30 years, it grows to about 7,612. Left for 40 years, it grows to about 14,974. The rate did not change, but the time did, and the time is doing most of the work.
That is why starting early beats starting big, for most people, and why waiting to save "until you earn more" can cost more than it appears to. The guide on setting financial goals shows how to put a start date on a plan.
Compounding works against you too
Compound interest applies to debt as well. A loan that charges interest and is not paid down grows in the same way. Credit card balances, in particular, can compound quickly, because the unpaid interest is added to the balance and then charges its own interest.
The same arithmetic that rewards saving early punishes debt left to grow. Paying off the highest-cost debt first is often the best return available to someone who has both debt and savings, because it removes the compounding that works against them.
Compounding in investing
Investments do not earn a fixed interest rate. Their returns change from year to year, sometimes sharply. Compounding still applies, because the returns in one year are added to the balance and earn returns in later years. But the path matters. A large fall in one year needs a larger rise in later years to recover, so the average return does not tell the whole story.
Suppose an investment gains 50 percent one year and loses 50 percent the next. The average is zero, but the balance ends lower than it started. Starting with 100, the first year makes it 150, and the second year takes it down to 75. The loss is harder to recover from than it looks, because the second fall is taken from a larger base.
This is why the guide on risk and return and the guide on diversification matter alongside the maths of compounding. Steady returns compound more reliably than erratic ones of the same average.
Inflation takes its share
A savings account that pays 5 percent does not grow your purchasing power by 5 percent if prices rise by 6 percent in the same year. The real return is roughly the interest rate minus inflation. The guide on inflation and your money explains how to think about that difference.
Compound interest makes growth look large in nominal terms. A measure of what the money can buy is more useful when you plan for a real goal.
The rule of 72
A quick way to estimate how long money takes to double is the rule of 72. Divide 72 by the annual rate, and you get roughly the number of years. At 8 percent, 72 divided by 8 is 9, so money doubles in about nine years. At 12 percent, it doubles in about six. The rule is an approximation, most accurate for rates between about 6 and 10 percent, but it is useful for comparing options quickly.
Practical steps
- Start early, even with a small amount. Time does more work than the size of the first deposit.
- Keep costs low. Fees are taken from the balance each year, so they compound against you in the same way interest compounds for you. A fee of 1 percent a year can take a large share of long-term growth.
- Reinvest the returns if your plan allows it. Taking the interest out each year stops the compounding.
- Check the rate and the compounding period. A rate quoted yearly may compound monthly, which gives a slightly higher effective rate. Ask what the effective annual rate is.
- Pay down high-cost debt first, because that compounding is working against you.
Common mistakes
Confusing the rate with the return. A high stated rate can compound more slowly than it looks if fees, taxes or inflation take a share each year.
Assuming steady growth. Investment returns vary. Plan for the bad years as well as the good ones.
Stopping the plan when the balance looks small. The early years of compounding look slow. The growth comes later, which is why patience matters.
Ignoring the effect of withdrawals. Taking money out early removes the balance that would have compounded. A small withdrawal early can cost much more than its face value later.
Key takeaways
Compound interest is interest earned on interest, and it grows balances at an increasing pace. The formula is principal times one plus the rate, raised to the number of periods. Time is the largest factor in the result, so starting early matters more than the rate. Compounding also works on debt, so high-cost debt should be paid down first. Keep costs low, reinvest where you can, and remember that real investment returns are uneven, which makes the path as important as the average.
This guide is for general information, not financial advice. See the disclaimer.