How compound interest works
Why money grows faster when returns earn returns — and why the same effect makes debt expensive. Includes the formula, the Rule of 72 and realistic examples.
Compound interest is interest that earns interest. That sounds small until you give it time. A balance growing at 7% a year does not add the same dollar amount each year; it adds a little more, because last year's interest is now part of the balance.
The same maths works in reverse on a credit card. The balance does not just sit there while you pay interest — the interest joins the balance and starts charging interest too.
Simple interest vs compound interest
With simple interest, you earn a fixed percentage of the original amount each period.
- Invest $1,000 at 7% simple interest.
- You earn $70 a year, every year.
- After 20 years you have $2,400.
With compound interest, you earn 7% of the current balance.
- Invest $1,000 at 7%, compounded annually.
- Year 1 ends at $1,070.
- Year 2 earns 7% of $1,070, not $1,000.
- After 20 years you have about $3,870.
The difference is not the rate. It is whether the return is allowed to compound.
The formula
For a lump sum with no additional contributions:
A = P × (1 + r / n)^(n × t)
- P is the starting principal.
- r is the annual rate as a decimal.
- n is the number of compounding periods per year.
- t is the number of years.
- A is the ending balance.
If $5,000 grows at 6% for 10 years, compounded monthly:
- r / n = 0.06 / 12 = 0.005
- n × t = 120
- A = 5,000 × 1.005^120 ≈ $9,096.98
Monthly compounding produces slightly more than annual compounding at the same nominal rate, because interest is added more often.
The Rule of 72
A quick estimate: divide 72 by the annual return to approximate the years needed to double your money.
- At 6%, about 12 years.
- At 8%, about 9 years.
- At 12%, about 6 years.
The rule is rough, and it works best for moderate rates. It is still useful for sanity-checking a projection.
Regular contributions change the curve
Most savings plans are not a single lump sum. They add money every month. Those contributions also compound.
If you save $200 a month at a 6% annual return, after 20 years you will have contributed $48,000. The projected balance is higher because each contribution has its own mini compounding timeline. Contributions made earlier have more time to grow than contributions made near the end.
Our compound interest calculator shows the year-by-year split between contributions and interest. That split is often the most useful part: it shows when growth starts doing more work than deposits.
Compounding frequency is not the main lever
Annual, quarterly and monthly compounding produce different results, but the gap is usually small. The bigger levers are:
- Time. Starting earlier usually beats chasing a slightly higher rate.
- Contribution rate. Regular deposits matter, especially in the early years.
- Fees and taxes. A 1% fee or a tax drag reduces the effective return.
- Risk. A higher expected return usually comes with more volatility.
A savings account might pay a modest rate with little risk. A stock portfolio might have a higher long-run expected return but can fall sharply along the way. Compounding assumes you stay invested through those falls.
The debt version
Compound interest is not automatically good. If you carry a credit card balance at 20% APR, the interest is added to the balance and starts costing interest too. That is why a minimum payment can take years to clear a relatively small balance.
The credit card payoff calculator shows how much interest a fixed payment saves compared with a minimum payment.
What projections leave out
A constant annual return is a modeling convenience, not a promise. Real investments do not deliver 7% every year. They deliver a mix of good and bad years, and the order matters when you are adding or withdrawing money.
Projections also usually ignore:
- inflation, which reduces purchasing power;
- taxes on interest, dividends or gains;
- account fees and fund expense ratios;
- the risk of needing the money during a downturn.
Use a range of returns rather than one number. If a goal depends on a 9% return every year for 30 years, the plan is fragile.
A practical way to use it
- Pick a realistic return range, not the best historical year.
- Include the fees you actually pay.
- Model the contribution you can sustain, not the one you hope to make.
- Check what happens if returns are 2% lower.
- Keep an emergency fund outside the projection.
Compound interest rewards patience and consistency. It does not reward precision to the second decimal place. For a savings target, try the savings goal calculator to turn the idea into a monthly number.