What is compound interest?
Compound interest is the math behind money that grows because the growth itself grows. You start with a principal. It earns interest. Next period, the interest earns interest too. Then that earns interest. Keep doing this for a few decades and you get a number that doesn't look like it should be right.
Albert Einstein supposedly called it the eighth wonder of the world. He probably didn't actually say that, but the math doesn't care who said what — it just keeps doing its thing. If you understand compounding, you understand most of personal finance. If you don't, you'll spend your working life confused about why some people retire comfortably and others don't, despite earning similar salaries.
Here's the part most people miss: compound interest works both directions. The same math that makes your retirement account double every ten years also makes credit card debt double every four. The Compound Interest Calculator on this page handles the friendly version — money you put in, money you get out. The unfriendly version uses the same formula with the same speed.
How to use the Compound Interest Calculator
The Compound Interest Calculator wants four numbers and gives you one back. Type them in any order; the result updates as you go.
- Enter the principal — the money you're starting with
- Enter the annual interest rate as a percentage (7 means 7%, not 0.07)
- Pick the compounding frequency from the dropdown (annually, semi-annually, quarterly, monthly, weekly, or daily)
- Enter the number of years
The future value appears in the green box. That's everything you'd have at the end — principal plus all the accumulated interest. Nothing is sent anywhere; the math runs in your browser. No sign-up, no email, no "create a free account to see your results." Free is a fact.
The formula behind compound interest
The classical compound interest formula is short enough to fit on a napkin:
A = P(1 + r/n)nt
Where:
- A is the final amount (what we're solving for)
- P is the principal (what you start with)
- r is the annual interest rate as a decimal (7% becomes 0.07)
- n is the number of compounding periods per year
- t is the time in years
The dial that matters most is t. Time is the variable doing the real work — that's why people who start saving at 25 retire dramatically richer than people who start at 35, even when the older saver puts in more money in absolute terms.
Worked example: $10,000 at 7% for 20 years
Let's run a real one. You put $10,000 into an account that earns 7% annually, compounded monthly, and leave it alone for 20 years. No additional deposits, no withdrawals.
A = 10,000 × (1 + 0.07/12)12 × 20 = $40,387.39
Your $10,000 became $40,387. The math earned you $30,387 in interest while you did nothing.
Now compare that to simple interest at the same rate. Simple interest only pays you on the original principal — never on the accumulated interest. The formula is I = P × r × t, so over 20 years at 7% you'd earn $14,000 in interest on top of your $10,000, for a total of $24,000.
The difference: $40,387 vs $24,000. Compounding gave you an extra $16,387 for doing nothing differently except letting interest earn interest. That gap widens every year you extend the timeline. It's the whole reason index-fund investing works.
How time and frequency multiply your money
The table below shows what $1,000 grows into at 7% across different timeframes and compounding frequencies. Read it slowly. The numbers tell a story.
| Time | Annual compounding | Monthly compounding | Daily compounding |
|---|---|---|---|
| 5 years | $1,402.55 | $1,417.63 | $1,419.02 |
| 10 years | $1,967.15 | $2,009.66 | $2,013.62 |
| 20 years | $3,869.68 | $4,038.74 | $4,054.66 |
| 30 years | $7,612.26 | $8,116.50 | $8,164.65 |
| 40 years | $14,974.46 | $16,310.39 | $16,437.46 |
Two things should jump out:
First, the curve isn't a curve early on. After five years, $1,000 at 7% gives you a respectable $402 in interest. After ten years, it's roughly $1,000 in interest. But after forty years? You're at roughly $15,000 in interest on a $1,000 principal. The growth between year 30 and year 40 alone is bigger than everything that happened in the first 20 years combined. That's exponential growth doing what exponential growth does.
Second, compounding frequency matters less than people think. Switching from annual to daily compounding at 7% over 40 years adds about $1,500 — meaningful but not life-changing. Switching from 20 years to 40 years adds $12,000. If you have to pick one variable to push on, push on time, not frequency.
The Rule of 72
You don't need a calculator to ballpark compound growth. The Rule of 72 is the trick every investor learns early:
Years to double = 72 ÷ interest rate
At 6%, your money doubles in 12 years (72 ÷ 6). At 9%, it doubles in 8 years. At 12%, in 6 years. At 3% (a typical savings account), it takes 24 years to double.
This is why even small changes in interest rate matter enormously over a career. A 401(k) earning 8% doubles every nine years. The same money earning 5% doubles every fourteen. Across a 40-year career, the 8% account doubles four-and-a-half times. The 5% account barely doubles three times. Same starting principal, very different retirements.
Compound interest cuts both ways
Everything above assumes you're the lender — the bank pays you, and the math works in your favor. Flip the role and the same formula becomes the case for never carrying credit card debt.
A $5,000 credit card balance at 22% APR, compounded daily, with no payments? That becomes $6,225 in 12 months, $11,597 in 4 years, and $26,898 in 10 years. Credit card companies aren't being evil. They're running the same formula your retirement account runs. They're just on the receiving end.
This is why financial advisors are almost universally allergic to credit card debt: the math is structurally tilted against the borrower in a way that no amount of budgeting brilliance can outrun. Pay it off, then go invest. If you want to see the same numbers in the other direction, the Loan Calculator shows what a structured monthly payment looks like instead of letting compounding run wild.
Related calculations
Compound interest sits at the center of a small family of money tools:
- Simple Interest Calculator — for short-term loans, bonds, or any setting where interest doesn't get added to the principal. Side-by-side this with compound to see the gap.
- Savings Calculator — when you're adding money regularly (e.g. $500/month into a retirement account), use this instead. It handles the recurring-deposit case that the compound interest formula above doesn't.
- Loan Calculator — the same compounding math applied to amortizing debt, with a monthly payment instead of a lump sum at the end.
Frequently asked questions
What's the difference between APR and APY?
APR (annual percentage rate) is the stated annual rate before compounding. APY (annual percentage yield) is the effective rate after compounding is applied. A savings account advertising "5.00% APR compounded daily" actually pays a 5.13% APY. When comparing accounts, always compare APY to APY — that's the apples-to-apples number.
Why does monthly compounding only beat annual by a little?
Diminishing returns. The first jump (from annual to monthly) captures most of the benefit because you're going from one compounding event per year to twelve. After that, going from monthly to daily is going from 12 to 365 events — more compounding, but on increasingly tiny slices of interest. The limit case is "continuous compounding" using ert, which is only marginally better than daily.
Does compound interest apply to stocks?
Sort of. Stocks don't pay a fixed interest rate, so the formula doesn't apply literally. But if you reinvest dividends and the stock appreciates, you're getting a compounding effect — gains on your gains. Long-term S&P 500 returns average around 10% nominal, 7% real (after inflation). Run those numbers through the calculator and you'll see why "buy and hold" became financial gospel.
How does inflation affect these numbers?
Inflation is compounding working in reverse on your purchasing power. At 3% inflation, $100 today is worth about $74 in ten years. So a 7% nominal return is really a 4% "real" return after inflation. When you see scary-looking compound interest projections (like $1,000 becoming $16,000 over 40 years), divide by inflation to get the real-world number. Even after inflation, the gains are still substantial — they're just less dramatic than the headline figure.
What's a realistic compound interest rate to expect?
Depends entirely on where the money sits:
- Checking account: 0.01% (basically zero)
- High-yield savings: 4% to 5% in 2024-2025; historically closer to 1% to 2%
- Certificate of deposit: 4% to 5.5% for 12-month terms recently
- U.S. Treasury bonds: 4% to 5%
- Stock market (S&P 500 average): around 10% nominal, 7% real, very volatile year to year
The calculator doesn't care which one you plug in — but real-world results depend a lot on whether you stick to your chosen rate through downturns.
Can I add deposits to a compound interest calculation?
Not this calculator — it solves the lump-sum case (one deposit, compound, wait). For the case where you're adding money every month (a 401(k), an IRA, a recurring savings transfer), use the Savings Calculator. The math is a separate formula — the future value of an annuity — and the result is usually much bigger than people expect, because every monthly deposit gets its own compounding tail.
Why do banks compound daily instead of monthly?
Daily compounding is marginally better for the saver and marginally worse for the bank, but the difference is small enough that it's mostly a marketing choice. "Compounded daily" sounds better than "compounded monthly," and banks compete on these surface details. The actual APY is what matters; the compounding frequency is a footnote unless you're carrying very large balances.
How accurate is the Rule of 72?
Very accurate for rates between 5% and 12%, which covers most realistic investment scenarios. Above 15%, the rule starts undershooting (real doubling time is faster). Below 3%, it overshoots slightly. For a quick mental check, 72 ÷ rate is reliable to within a fraction of a year for any normal context. The Compound Interest Calculator gives you the exact number; the Rule of 72 gives you the napkin estimate.