What is compound interest?
Compound interest is interest calculated on both your original money (the principal) and on the interest it has already earned. In other words, it's interest on your interest. Each year's growth becomes part of the base for the next year's growth, which is why balances curve upward over long periods instead of rising in a straight line.
Albert Einstein is often credited with calling compound interest "the eighth wonder of the world," but there's no record that he ever said it. The idea holds up anyway: given enough time, the interest you earn can grow larger than everything you put in.
How to use this calculator
- Initial Investment: the amount you start with today. Use 0 if you're starting from scratch.
- Monthly Contribution: how much you add at the end of each month.
- Length of Time: how many years the money stays invested.
- Estimated Interest Rate: the average yearly return you expect. A savings account might pay a few percent; a diversified stock portfolio has historically averaged more, but with large ups and downs along the way.
- Compound Frequency: how often interest is added to the balance (monthly, quarterly, twice a year or yearly).
Results update as you type. The chart splits every year's balance into your starting principal, your contributions and the interest earned, so you can see when interest starts doing most of the work.
Worked example
These are the calculator's default inputs, so you can reproduce them by loading the page.
You invest $1,000 today and add $100 a month for 10 years at 7%, compounded monthly:
- Total balance: $19,318
- Starting principal: $1,000
- Contributions: $12,000 ($100 × 120 months)
- Total invested: $13,000 (principal + contributions)
- Interest earned: $6,318
Now change the time to 30 years. The balance grows to $130,114, and $93,114 of that is interest: more than 70% of the final balance is money you never deposited.
The formula
The calculator converts your compounding frequency into an equivalent monthly rate, then steps through every month:
Effective annual rate EAR = (1 + r / n)^n - 1
Monthly rate i = (1 + EAR)^(1/12) - 1
Each month B = B × (1 + i) + monthly contribution
Here r is the yearly interest rate and n is how many times a year interest compounds. Contributions are added at the end of each month. With no monthly contributions, this gives the same result as the textbook formula A = P(1 + r/n)^(nt).
Does compounding frequency matter?
Less than most people think. Here's $10,000 left for 10 years at 6%:
| Compounding | Balance after 10 years |
|---|---|
| Monthly | $18,194 |
| Quarterly | $18,140 |
| Semi-annually | $18,061 |
| Annually | $17,908 |
The gap between monthly and yearly compounding is under $300. The rate you earn and how long you stay invested matter far more.
The Rule of 72
A quick mental shortcut: divide 72 by your yearly return to estimate how many years it takes your money to double. At 8%, 72 / 8 = 9, so money doubles roughly every 9 years without any new deposits. The rule is an approximation that works best for rates between about 4% and 12%.
The cost of waiting
Time is the most powerful input in the calculator. Compare two people who each invest $300 a month at 7% until age 65:
- Starting at 25 (40 years): $787,444 from $144,000 of contributions.
- Starting at 35 (30 years): $365,991 from $108,000 of contributions.
The early starter contributes only $36,000 more but ends with about $421,000 more, because their money had an extra decade to compound.
Assumptions and limitations
- Constant return: the calculator applies the same rate every year. Real investments rise and fall, and the order of good and bad years affects the outcome.
- No taxes or fees: account fees, fund expense ratios and taxes on gains all reduce real-world results.
- Not adjusted for inflation: results are in future dollars. To see today's purchasing power, subtract expected inflation from the rate (for example, 7% returns with 3% inflation is roughly a 4% "real" rate).
Frequently asked questions
What interest rate should I use?
Use the rate that matches where the money will actually be. For a high-yield savings account or CD, use its stated APY. For a stock portfolio, many people test a range, such as 5%, 7% and 9%, rather than relying on a single number, because no future return is guaranteed.
What's the difference between simple and compound interest?
Simple interest is paid only on the original principal, so it grows by the same amount every year. Compound interest is also paid on past interest, so the yearly growth itself keeps getting bigger.
Are contributions made at the start or the end of each month?
At the end. If you contribute at the start of each month instead, your real balance would be slightly higher, because each deposit earns one extra month of interest.
Does this account for inflation or taxes?
No. Enter an inflation-adjusted ("real") rate to see results in today's dollars, and keep in mind that taxes and fees will lower the final balance unless the money is in a tax-advantaged account.