Compound interest is interest earned on your earlier interest as well as on the original amount. Each period's interest is added to the balance, so the next period's interest is calculated on a bigger number. Over short times it looks like ordinary interest; over decades it is the difference between steady and explosive growth. The same effect works against you on debt that is left to grow. Try your own numbers in the Compound Interest Calculator.
The formula
A = P × (1 + r/n)^(n × t)
A is the final amount, P the starting amount, r the annual rate as a decimal, n the number of times interest is added per year and t the number of years.
Example: $10,000 at 5% for 10 years. With yearly compounding, A = 10,000 × 1.05^10 = $16,288.95. Simple interest would give only $15,000.
More frequent compounding
The more often interest is added, the more you earn, but the gains shrink quickly:
| Compounding | Times a year | Balance after 10 years | Interest earned |
|---|---|---|---|
| Annually | 1 | $16,288.95 | $6,288.95 |
| Quarterly | 4 | $16,436.19 | $6,436.19 |
| Monthly | 12 | $16,470.09 | $6,470.09 |
| Daily | 365 | $16,486.65 | $6,486.65 |
| Continuously | ∞ | $16,487.21 | $6,487.21 |
Going from yearly to monthly adds about $181.15; going from monthly to daily adds only $16.55. The theoretical limit is continuous compounding, A = P × e^(r × t).
APR versus APY
The APR (or nominal rate) ignores compounding. The APY (annual percentage yield) includes it: APY = (1 + r/n)^n − 1. A 5% rate compounded monthly has an APY of 5.116%. When comparing savings accounts, compare APYs; when comparing loans, see the APR Calculator.
The Rule of 72
To estimate how long money takes to double, divide 72 by the annual percentage rate. At 5% that is 72 / 5 = 14.4 years. The exact figure is 14.2 years, so the shortcut is close enough for quick planning, and it works best for rates between about 4% and 12%.
Regular contributions
Adding money regularly multiplies the effect. Saving $200 a month at 7% a year, compounded monthly:
| Years | You deposit | You end with | Growth |
|---|---|---|---|
| 20 | $48,000.00 | $104,185.33 | $56,185.33 |
| 30 | $72,000.00 | $243,994.20 | $171,994.20 |
Ten more years adds only 50% more deposits ($24,000.00), but the balance is more than 2.3 times larger, because the early deposits get decades to compound. This is why starting early matters more than saving more later. See what your plan could become with the Savings Calculator and the Investment Calculator.
Compounding works against debt, too
A credit card balance charged 20% APR and compounded daily grows quickly if only the minimum is paid. Paying down high-interest debt is often the best "return" available; see How Loan Amortization Works for how fixed loans are paid off.
Caveats
- Returns are not guaranteed. The examples assume a constant rate. Real investments rise and fall, and past results do not predict future ones.
- Fees and taxes reduce growth. A 1% yearly fee on a 7% return cuts your result a lot over decades.
- Inflation matters. A 5% balance growth in an economy with 3% inflation is about 2% real growth.
The Interest Calculator handles simple interest and compounding side by side. Related terms: Compound interest, APY, APR and Inflation.