How to calculate compound interest
Updated on June 18, 2026 · by Rafael Rossi
Compound interest is "interest on interest": each period, the return is calculated on the full accumulated balance, not just the amount you started with. That makes growth exponential rather than linear — slow at first, then faster and faster.
The phrase gets repeated endlessly, but almost nobody has an intuition calibrated to the size of the effect. This guide uses real numbers to show exactly where intuition goes wrong.
The formula
Balance = Principal × (1 + i)n
Where i is the rate per period (as a decimal) and n is the number of periods. With regular contributions, add the annuity term:
+ PMT × [((1+i)n − 1) / i]
The two halves answer different questions. The first tells you what the money already invested will become; the second tells you what your monthly discipline will become. Over long horizons the second is usually far larger — which is why starting small is not a problem, but starting late is.
Worked example
$1,000 to start plus $300 a month, at 8% a year compounded monthly:
| Time | Contributed | Balance | Interest alone |
|---|---|---|---|
| 1 year | $4,600 | $4,818 | $218 |
| 5 years | $19,000 | $23,533 | $4,533 |
| 10 years | $37,000 | $57,103 | $20,103 |
| 20 years | $73,000 | $181,633 | $108,633 |
| 30 years | $109,000 | $458,044 | $349,044 |
Watch the proportion move. After one year, interest is under 5% of what you put in. After thirty, interest is more than three times everything you ever contributed. The money working has overtaken the person working.
The tenth year earns nearly 20 times the first
This is the number that changes minds. In year one of the simulation above, interest comes to $218. In year ten — from the identical $3,600 contributed — that single year adds $4,225.
Same monthly effort, nineteen times the result, and the only difference is how long the money has been working. People who quit in year three because "it isn't growing" walk away right before the part that matters.
Contribute more, or earn more? It depends on the horizon
Practical question: is it better to add $100 to the monthly contribution, or to find a full extra percentage point of return? At US-typical rates the answer is more one-sided than most people expect.
| Horizon | +$100/month adds | +1 percentage point adds | Winner |
|---|---|---|---|
| 10 years | +$18,295 | +$3,402 | the contribution, by 5× |
| 20 years | +$58,902 | +$24,742 | the contribution, by 2.4× |
| 30 years | +$149,036 | +$105,910 | the contribution, still |
The crossover — where the extra point of return finally beats the extra $100 a month — does not arrive until around year 39. For any horizon a normal person actually plans for, the thing you control beats the thing you chase. Which means taking on real risk to squeeze out an extra point for a five-year goal is trading danger for almost nothing.
Common mistake: APR is not the rate you earn
A nominal 8% APR compounded monthly does not return 8% over the year — it returns 8.30%, because each month's interest earns interest too. That figure is the APY (annual percentage yield), and the gap widens with the rate.
Lenders exploit the asymmetry: institutions quote APY when they want your deposit and APR when they are lending to you, because APY looks bigger and APR looks smaller. Always check which one you are reading.
The same math runs against you
Compound interest has no loyalty. A $1,000 credit card balance at 24% APR, left untouched for a year, becomes $1,268 — a 26.8% effective cost, not 24%. Carry it for five years and it reaches $3,281.
That is why the priority order is almost always the same: clear expensive debt before investing. No ordinary investment pays what a credit card charges.
What the math leaves out
- Taxes. Gains in a taxable account are taxed as they are realised; the same contributions in a 401(k) or IRA compound untaxed, which over 30 years is worth more than most rate-shopping.
- Fees. Expense ratios come out of the balance every year — and they compound too, in the wrong direction. A 1% annual fee over 30 years consumes roughly a quarter of the final balance.
- Inflation. $458,000 in thirty years does not buy what $458,000 buys today. To think in purchasing power, use a real rate, net of inflation.
Frequently asked questions
How long until my money doubles? The rule of 72 is a good approximation: divide 72 by the rate as a percentage. At 8%, that is 9 years — and the exact answer is also 9.0 years. The rule is at its most accurate right around the rates people actually earn.
How is this different from simple interest? With simple interest the return is always calculated on the original principal, so growth is a straight line. With compound interest it is calculated on the balance, so growth is a curve that accelerates. Over short horizons the difference is small; over long ones it is the difference between doubling and multiplying tenfold.
Does daily compounding beat monthly? It does, but by less than people expect, and there is a ceiling. The more often interest compounds, the closer the result gets to the limit of continuous compounding — a nominal 12% can never exceed 12.750% effective, no matter how finely you slice the period.
Is it worth starting with $100? Yes, though not because of the $100: it is worth it because the monthly contribution does the heavy lifting for the first fifteen years or more. A small starting balance costs you far less than starting five years later.