What is compound interest?
Compound interest is interest earned on interest. Each period, your balance grows — and the next period’s interest is calculated on that bigger balance. Early on the effect looks small; over decades it becomes the dominant force in your savings. Albert Einstein probably never called it the eighth wonder of the world, but the math behind the legend is real.
The formula
For a lump sum: A = P (1 + r/n)ⁿᵗ, where P is the starting amount, r the annual rate, n the number of compounding periods per year, and t the years. This calculator compounds monthly and adds your contribution at the end of each month.
Worked example: $5,000 plus $300 a month
Start with $5,000, add $300 every month, and earn 7% a year for 20 years. You’ll have contributed $77,000 of your own money — but the balance grows to about $176,000. More than half of the final amount ($99,000+) is growth, not deposits. That’s compounding doing the heavy lifting.
The cost of waiting ten years
| Start age | Contributed by 65 | Balance at 65 (7%) |
|---|---|---|
| 25 | $96,000 | ~$525,000 |
| 35 | $72,000 | ~$244,000 |
Both savers put away $200/month at 7%. The one who started at 25 contributes only $24,000 more, yet retires with roughly $280,000 more. Time in the market is the single biggest input you control — more than the rate, more than the amount.
The Rule of 72
Divide 72 by your annual return to estimate how long money takes to double. At 7%, that’s about every 10 years — and indeed $10,000 at 7% grows to about $20,100 in 10 years with monthly compounding. At 3% it takes ~24 years; at 10%, ~7 years.
Does compounding frequency matter?
Less than most people think. $10,000 at 7% for 10 years grows to $19,672 compounded annually and $20,097 compounded monthly — a difference of about 2%. What moves the needle far more is the rate itself, your contributions, and how long you stay invested. When comparing savings accounts, look at APY (which already includes compounding) rather than the nominal rate.
Where you’ll meet compound interest
Working for you: high-yield savings accounts, CDs, reinvested dividends, and long-run stock index funds (where ~7% is a commonly cited historical average after inflation — useful for planning, never guaranteed). Working against you: credit-card balances, where 20%+ APRs compound on what you owe — the same math in reverse. If that’s your situation, start with the credit card payoff calculator or the debt payoff calculator. To turn a target amount into a monthly savings plan, use the savings goal calculator, and for the long game see the retirement calculator.
Frequently asked questions
How is compound interest calculated?
Each period, interest is calculated on the current balance — including previously earned interest — using A = P(1 + r/n)^(nt). This calculator compounds monthly and adds contributions at the end of each month.
What is the Rule of 72?
A quick mental shortcut: divide 72 by the annual return to estimate the years needed for money to double. At 8%, roughly 9 years; at 6%, about 12.
How much will $10,000 be worth in 10 years at 7%?
About $20,100 with monthly compounding (about $19,700 compounded annually) — roughly doubling, exactly as the Rule of 72 predicts.
What rate of return should I assume?
For long-term stock index investing, planners often model 6–8% annually; savings accounts currently earn much less. Historical averages are useful for planning but never guaranteed — try a range of rates with the slider to see best and worst cases.
What's the difference between simple and compound interest?
Simple interest is always calculated on the original principal only. Compound interest is calculated on principal plus accumulated interest, so it grows faster — dramatically so over long periods.
Is interest I earn taxed?
Generally yes — bank interest is typically taxable income, and investment growth may be taxed as capital gains, unless held in tax-advantaged retirement accounts. This calculator shows pre-tax growth.
Can compound interest work against me?
Yes. Credit-card debt compounds the same way in reverse: interest is charged on your balance including previous interest. That's why carrying a 20%+ APR balance grows so quickly and why paying it down beats most investments.
Do monthly contributions change the math a lot?
Enormously. In the example above, $300/month accounts for most of the final balance. Consistent contributions plus time beat trying to pick the perfect rate.