How Compound Interest Works
Simple interest pays you only on the money you originally deposited. Compound interest pays you on your deposit and on all of the interest you have already earned. In the first few years the difference is small, but because each year's interest becomes part of the base for next year's interest, the growth curve bends upward over time. That is why the same savings habit started ten years earlier can end with roughly twice the balance.
This calculator adds your monthly contribution at the end of each month and applies interest according to the compounding frequency you choose. When the compounding frequency is not monthly, we convert the annual rate into the equivalent monthly growth rate, so the result matches what a bank or brokerage statement would show.
The formula
Here P is the starting amount, C is the monthly contribution, r is the monthly growth rate and n is the number of months. The first term grows your starting balance; the second term is the future value of a series of equal deposits, known in finance as an annuity.
Worked example
Suppose you start with $5,000, add $200 every month and earn 7% a year compounded monthly for 20 years. You personally contribute $5,000 + (240 × $200) = $53,000. The account grows to roughly $124,000, which means about $71,000 — more than half of the final balance — comes from interest rather than from your own pocket. Extend the same plan to 30 years and the balance rises to roughly $285,000, even though you contributed only $24,000 more.
| Time invested | You contribute | Balance at 7% |
|---|---|---|
| 10 years | $29,000 | ≈ $44,600 |
| 20 years | $53,000 | ≈ $124,000 |
| 30 years | $77,000 | ≈ $284,600 |
| 40 years | $101,000 | ≈ $606,000 |
The Rule of 72
A quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes for money to double. At 6% money doubles in about 12 years; at 9% in about 8 years; at 3% it takes about 24 years. The rule works best for rates between 4% and 12% and is a handy way to sanity-check any investment promise you hear.
Four ways to make compounding work harder
- Start early. Time is the most powerful variable in the formula because it sits in the exponent.
- Contribute automatically. A fixed monthly transfer removes the temptation to skip a month.
- Keep costs low. A 1% annual fee can consume a quarter or more of your final balance over 30 years.
- Reinvest the returns. Withdrawing interest or dividends turns compound growth back into simple growth.
Limitations to keep in mind
Real investments do not grow at a smooth, constant rate. Stock returns vary widely from year to year, savings account rates change with central-bank policy, and taxes and inflation reduce what you actually keep. Use this calculator to compare scenarios and build intuition, then pair it with our inflation calculator to see what a future balance is worth in today's money.
Frequently Asked Questions
What is a realistic interest rate to use?
High-yield savings accounts typically pay a few percent a year, government bonds somewhat more, and broad stock-market index funds have historically averaged roughly 6–10% per year over long periods, with large swings between years. For planning, many people use a conservative 5–7% for a stock-heavy portfolio.
Does compounding frequency matter much?
Less than most people think. At 7% a year, monthly compounding gives an effective annual rate of about 7.23% and daily compounding about 7.25%. The rate itself, your contributions and the number of years matter far more.
Are contributions added at the start or end of the month?
This calculator assumes contributions are made at the end of each month, which is the standard convention. Contributing at the start of each month would produce a slightly higher balance.
Does this account for taxes or inflation?
No. Results are shown in nominal dollars before tax. Use the inflation calculator to convert a future balance into today's purchasing power.
Disclaimer: This calculator is for educational purposes only and does not constitute financial, tax or investment advice. Results are estimates based on the assumptions you enter; real returns, rates, fees and taxes vary. Consider speaking with a licensed financial professional before making decisions.
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