How compound interest works
Compound interest is interest earned on your interest. Each time interest is credited, it's added to your balance, and the next round of interest is calculated on that larger balance. Over short periods the difference from simple interest is small; over decades it does most of the work.
The compound interest formula
For a single deposit with no additions, the balance after t years is:
A = P × (1 + r/n)n×t
- 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 (12 for monthly, 365 for daily)
- t is the number of years
This calculator also adds a deposit at the end of every month, so it computes the balance month by month rather than with the single formula. At each compounding date the result matches the formula exactly.
Does compounding frequency matter?
A little, but less than most people expect. Here is $10,000 at 5% for 10 years with no extra deposits:
| Compounding | Balance after 10 years | APY |
|---|---|---|
| Annually | $16,289 | 5.00% |
| Quarterly | $16,436 | 5.09% |
| Monthly | $16,470 | 5.12% |
| Daily | $16,487 | 5.13% |
Going from annual to daily compounding adds about $200 over ten years. The interest rate, the amount you deposit and how long you leave it matter far more.
APY vs. APR
Banks advertise savings accounts and CDs by APY (annual percentage yield), which already includes the effect of compounding. Loans are usually quoted as APR, the nominal rate before compounding. When comparing two savings accounts, compare APYs: a 5.00% APY pays the same no matter how often it compounds.
If you know an account's APY rather than its nominal rate, enter the APY with annual compounding here to get the same result.
The Rule of 72
To estimate how long it takes money to double, divide 72 by the annual rate. At 5%, that's 72 ÷ 5 = 14.4 years; the exact figure with annual compounding is 14.2 years. The summary above shows the exact doubling time for your inputs.
Getting the most from compound interest
- Start early. Time is the exponent in the formula, so an extra five years of growth can be worth more than a larger deposit later.
- Deposit regularly. Monthly deposits give each dollar more time to earn interest than a single deposit at year end.
- Leave the interest in. Withdrawing interest turns compound growth back into simple interest.
- Watch taxes and inflation. Interest in a regular savings account is taxed as ordinary income each year, and inflation reduces what the final balance can buy. Tax-advantaged accounts such as IRAs and 401(k)s let growth compound without an annual tax bill.
Assumptions
The rate stays fixed for the whole period, deposits are made at the end of each month, and taxes, fees and inflation are not included. For investments whose returns vary from year to year, such as stock funds, try the investment calculator, which shows a best- and worst-case range.