What is compound interest?
Compound interest is interest earned on both your original deposit and on the interest that has already been added to it. With simple interest you earn the same dollar amount every year; with compound interest the amount grows each period because the base keeps getting larger. Over short periods the difference is small, but over decades it becomes the main driver of your balance.
$10,000 at 5% simple interest for 10 years earns $500 a year and ends at $15,000. The same $10,000 at 5% compounded annually ends at $16,288.95 — $1,289 more, purely from earning interest on interest.
The compound interest formula
For a single deposit:
A = P × (1 + r/n)n × t
A is the ending balance, P the principal, r the annual rate as a decimal, n the number of times interest compounds per year and t the number of years. When you also make regular deposits, each deposit compounds for the time remaining. For monthly deposits of PMT at an effective monthly rate i over m months, the deposits add:
PMT × [((1 + i)m − 1) / i]
If you deposit at the start of each month instead of the end, multiply that term by (1 + i), because each deposit earns one extra month of interest. Try the checkbox above: over five years, $250 a month at 4.5% grows to $16,786.39 with end-of-month deposits and $16,849.34 with start-of-month deposits.
When the compounding frequency differs from your deposit frequency (for example daily compounding with monthly deposits), the calculator converts the rate into the equivalent monthly rate, i = (1 + r/n)n/12 − 1, so every option is compared on the same footing. Our methodology page explains every assumption.
Does compounding frequency matter?
Here is $10,000 at a 5% stated rate for 10 years with no extra deposits:
| Compounding | Effective annual yield (APY) | Balance after 10 years |
|---|---|---|
| Annually | 5.000% | $16,288.95 |
| Semiannually | 5.062% | $16,386.16 |
| Quarterly | 5.095% | $16,436.19 |
| Monthly | 5.116% | $16,470.09 |
| Daily | 5.127% | $16,486.65 |
Moving from annual to daily compounding adds only about $198 over ten years. When you compare savings accounts, CDs or Treasury bills, focus on the APY and on how long you can leave the money invested — those matter much more than how often interest is credited.
The rule of 72
A quick way to estimate compounding without a calculator: divide 72 by the annual rate to get the approximate number of years for money to double.
| Annual rate | Rule of 72 estimate | Exact doubling time |
|---|---|---|
| 4% | 18.0 years | 17.7 years |
| 6% | 12.0 years | 11.9 years |
| 8% | 9.0 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
Where compound interest shows up
- High-yield savings accounts and CDs – usually compound daily or monthly and quote an APY.
- Treasury bills and bonds – interest compounds only if you reinvest it.
- Stock and ETF investing – not interest, but reinvested dividends and price growth compound the same way. See the DRIP calculator for dividend reinvestment.
- Debt – credit card balances compound against you, often daily at rates above 20%.
For a broader projection with inflation-adjusted results and yearly contribution increases, use the investment calculator.
Frequently asked questions
What is the compound interest formula?
For a single deposit, A = P × (1 + r/n)^(n×t), where P is the principal, r the annual interest rate as a decimal, n the number of compounding periods per year and t the number of years. Regular deposits add a future-value-of-annuity term on top of that.
Is daily compounding much better than monthly?
Only slightly. At 5% a year, monthly compounding gives an effective annual yield of about 5.116% and daily compounding about 5.127%. The interest rate and the length of time you stay invested matter far more than the compounding frequency.
What is the difference between APR and APY?
APR is the stated annual rate before compounding. APY (annual percentage yield) is the effective rate after compounding within the year. Savings accounts in the US are required to disclose APY, so when comparing accounts you can compare APYs directly.
Does compound interest apply to stock investments?
Stocks do not pay interest, but reinvested dividends and price growth compound in the same way: gains earn further gains. The difference is that stock returns vary from year to year, while a savings account or CD pays a known rate.
What is the rule of 72?
Divide 72 by the annual interest rate to estimate how many years it takes money to double. At 6%, money doubles in roughly 72 ÷ 6 = 12 years. It is a quick approximation that works best for rates between about 4% and 12%.
Not financial advice. These figures are hypothetical and assume a constant rate of return. Real investments go up and down, past performance does not predict future results, and taxes and fees vary. Consider speaking with a licensed financial professional before making investment decisions. See our full disclaimer.