Compound interest is interest earned on both your original money and the interest it has already earned. Each time interest is credited, it joins the balance and starts earning interest itself. The result is growth that speeds up over time: $10,000 at 5% a year becomes $16,289 after 10 years, $26,533 after 20 and $43,219 after 30, even though the rate never changes.
The compound interest formula
For a single deposit with no further additions, the future balance is:
- A is the ending balance
- P is the starting principal
- r is the annual interest rate as a decimal (5% = 0.05)
- n is how many times per year interest compounds (1 annually, 12 monthly, 365 daily)
- t is the number of years
The interest earned is simply A − P. If you need to solve for the rate or the time instead, rearrange with logarithms or use the compound interest calculator, which handles every variable.
Worked example: $10,000 at 5% for 10 years
With annual compounding: A = 10,000 × 1.0510 = 10,000 × 1.62889 = $16,288.95. You earned $6,288.95 in interest, compared with $5,000 under simple interest.
Here is why the two differ. In year 1 both methods pay $500. In year 2 compound interest pays 5% of $10,500, or $525, while simple interest still pays $500. The gap is small at first but grows every year:
| Years | Simple interest balance | Compound balance (annual) | Extra from compounding |
|---|---|---|---|
| 1 | $10,500.00 | $10,500.00 | $0.00 |
| 5 | $12,500.00 | $12,762.82 | $262.82 |
| 10 | $15,000.00 | $16,288.95 | $1,288.95 |
| 20 | $20,000.00 | $26,532.98 | $6,532.98 |
| 30 | $25,000.00 | $43,219.42 | $18,219.42 |
Time is the biggest lever. The last 10 years of the 30-year period add more than the first 20 years combined. For a side-by-side with the simpler method, see the simple interest calculator.
How compounding frequency changes the result
More frequent compounding credits interest sooner, so it starts earning sooner. Same $10,000, same 5% nominal rate, same 10 years:
| Compounding | Periods per year (n) | Balance after 10 years |
|---|---|---|
| Annually | 1 | $16,288.95 |
| Quarterly | 4 | $16,436.19 |
| Monthly | 12 | $16,470.09 |
| Daily | 365 | $16,486.65 |
| Continuously | — | $16,487.21 |
The jump from annual to monthly is worth about $181; going from monthly to daily adds only $17. Continuous compounding, A = P × ert, is the mathematical limit and barely beats daily.
This is the reason banks quote APY (annual percentage yield) on savings: it converts any compounding frequency into one comparable annual figure. A 5% rate compounded monthly has an APY of 5.116%. The guide on APR vs. APY explains the conversion, and the effective annual rate calculator does it for any rate.
Adding regular contributions
Most people do not deposit once and walk away; they add money every month. Each deposit then compounds for however long it stays invested. For equal deposits at the end of each period, the future value is:
where PMT is the deposit, i is the rate per period (annual rate ÷ 12 for monthly) and N is the total number of deposits.
Example: $200 a month at a 7% annual return, compounded monthly.
i = 0.07 ÷ 12 = 0.0058333. After 30 years, N = 360 deposits.
FV = 200 × ((1.0058333)360 − 1) ÷ 0.0058333 = $243,994.
You contributed $72,000; the other $171,994 is compound growth.
Watch what happens as the time horizon stretches:
| Years of $200/month at 7% | Total contributed | Ending balance | Growth |
|---|---|---|---|
| 10 | $24,000 | $34,617 | $10,617 |
| 20 | $48,000 | $104,185 | $56,185 |
| 30 | $72,000 | $243,994 | $171,994 |
| 40 | $96,000 | $524,963 | $428,963 |
Ten more years of the same $200 deposits more than doubles the balance between year 30 and year 40. Starting early matters more than starting big. The savings calculator and future value of annuity calculator model deposits like these.
The Rule of 72
To estimate how long it takes money to double, divide 72 by the annual rate in percent:
The exact answer is ln(2) ÷ ln(1 + r). The shortcut is close across normal rates:
| Annual rate | Rule of 72 | Exact years (annual compounding) |
|---|---|---|
| 2% | 36.0 | 35.0 |
| 4% | 18.0 | 17.7 |
| 6% | 12.0 | 11.9 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
The same rule works in reverse for inflation: at 3% inflation, prices double in about 24 years. Try other rates with the Rule of 72 calculator.
What compound interest does not account for
The formula assumes a fixed rate, no withdrawals and no taxes. Real results differ for a few reasons:
- Variable returns. Stocks and funds do not earn a steady 7%. A sequence of good and bad years compounds to less than the average return suggests; see CAGR vs. average annual return.
- Taxes. Interest in a regular savings account is taxable each year, which reduces what stays invested. Tax-advantaged accounts such as a 401(k) or IRA let the full amount compound.
- Fees. A 1% annual fee comes off the return every year, so it compounds against you. Over 30 years it can consume about a quarter of the ending balance.
- Inflation. A balance that doubles in nominal dollars buys less if prices also rose. Subtract inflation from the return for a rough real growth rate.
Compound interest on debt
The same math works against borrowers. Credit card interest is charged on the unpaid balance, which includes last month’s interest, so an unpaid balance compounds. A 24% APR compounded monthly works out to about 26.8% a year in effective terms. Paying more than the minimum stops that cycle, as the guide to how credit card interest is calculated shows.
Quick steps to estimate your own growth
- Write down your starting balance, expected annual rate and number of years.
- Choose the compounding frequency your account uses (check the account disclosure; savings accounts usually compound daily or monthly).
- Apply A = P(1 + r/n)nt for the lump sum.
- Add the future value of any regular deposits.
- Reduce the rate for fees and taxes if they apply, and compare the result with inflation.
This guide explains the math of compound growth for educational purposes. It is not financial advice, and investment returns are not guaranteed; past performance does not predict future results.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is paid only on the original principal. Compound interest is paid on the principal plus all interest already credited. $10,000 at 5% for 30 years grows to $25,000 with simple interest but to $43,219 with annual compounding.
Does compounding more often make a big difference?
Less than most people expect. $10,000 at 5% for 10 years grows to $16,289 compounded annually and $16,487 compounded daily, a difference of about $198. The rate and the time invested matter far more than the frequency.
How long does it take money to double with compound interest?
Divide 72 by the annual rate in percent. At 6%, money doubles in about 72 ÷ 6 = 12 years; the exact answer is 11.9 years. The Rule of 72 is most accurate for rates between about 4% and 12%.
Do investments like index funds compound?
Their growth compounds in the sense that gains build on earlier gains when you reinvest dividends and leave the balance alone. Unlike a savings account, though, the return is not fixed and some years are negative, so the compound interest formula gives only an estimate.
Does compound interest work against me on debt?
Yes. Credit cards and other revolving debt charge interest on unpaid interest, so a balance you do not pay down grows faster than the stated APR suggests. A 24% APR compounded monthly is an effective rate of about 26.8% a year.