Your turn
Each lab is one step from the video. Slide, tap and compare.
Each lab isolates one idea. All figures are math examples with annual compounding (monthly for the card); real returns vary. Not financial advice.
Tap the buttons and slide the sliders.
Ava saves for 10 years, Ben for 30. Who has more at 65? Make your guess.
$50,000 contributed early vs. $150,000 contributed late, both at 8%. Pick a winner.
Ava starts early. Ben starts late. Who ends up with more? Guess!
Drag the years. Watch the coral part, the interest on interest, take over.
Each bar splits into principal, simple interest and interest on interest ($100 at 5%).
Slide the years. Watch the snowball and the pink part grow!
Double any dial for your own pile. Which one helps most?
Doubling P doubles A; doubling t usually does more over long periods, because t is the exponent.
Tap the buttons. Which one makes the biggest pile?
Pick a rate and count how many times $5,000 doubles in 36 years.
Compare the 72 ÷ rate estimate with the exact compound curve.
Pay nothing, or pay in full? Change the card’s rate too.
A $1,000 balance with no payments, compounded monthly at the APR you pick.
Tap the buttons. Watch the snow stop when it is all paid back!
Change the amount, the rate and Ben’s start age. How much of each pile is interest?
Deposits at the start of each year; Ava saves ages 25–34 only. Illustrative returns, not a forecast.
Slide the sliders. See who ends up with the bigger pile.
When you keep money in a bank, the bank gives you a little extra. That extra is called interest.
Next year, you get extra on your money. You also get extra on last year's extra! That is compound interest. Your money makes money, and that money makes more.
A snowball rolling down a hill picks up snow. The bigger it gets, the more snow it grabs. Money that earns interest grows the same way: slowly at first, then faster and faster.
Money that starts growing early has more time to grow. That is why starting early helps so much, even with a little money.
When grown-ups borrow money with a card and don't pay it back, the extra grows on what they owe. Paying it all back on time stops that snowball.
Compound interest is interest you earn on your interest. When you save money, the bank or investment pays you interest. That interest is added to your balance, and next time you earn interest on the bigger balance: your original money plus the interest you already earned.12
Here's the example the U.S. Securities and Exchange Commission uses for students. Put $100 in an account that earns 5% a year. After one year you have $105. After the second year you have $110.25: you earned $5 on your first $100, plus 25 cents on the $5 of interest.1 Twenty-five cents doesn't sound like much. But it keeps growing. Without adding another dime, you'd have more than $162 after 10 years and almost $340 after 25 years.1
That's the whole trick. Each year's growth builds on all the growth before it, so the money grows faster and faster, like a snowball rolling downhill.
The Consumer Financial Protection Bureau walks through it with $1,000 at 5%, with interest added once a year:2
| Year | Start of year | Interest (5%) | End of year |
|---|---|---|---|
| 1 | $1,000.00 | $50.00 | $1,050.00 |
| 2 | $1,050.00 | $52.50 | $1,102.50 |
| 3 | $1,102.50 | $55.13 | $1,157.63 |
Look at the interest column. It grows every year even though the rate stays at 5%, because the balance it's calculated on keeps getting bigger. The CFPB uses a few words you'll see everywhere:2
Working year by year gets slow. Thirty years of monthly interest would be 360 steps! Luckily, there's a formula for it:6
A = P (1 + r/n)n·t
If interest is added once a year, n = 1 and the formula becomes simply A = P(1 + r)t.6 Try it: $100 × 1.0510 ≈ $162.89, just like the SEC's example. Mathematicians call this kind of growth a geometric sequence: every step multiplies by the same number instead of adding the same amount.6
Simple interest is calculated on your original principal only. Compound interest is calculated on the principal plus the interest already added.67 Over a short time the difference is small. OpenStax's textbook example: $1,000 in a certificate of deposit (CD) at 4% for 3 years is worth $1,124.86 with compound interest, versus $1,120 with simple interest.6 Over longer times the gap grows:
| $5,000 at 5% for 5 years | Total interest |
|---|---|
| Simple interest ($250 every year) | $1,250.00 |
| Compounded once a year | $1,381.41 |
Figures from the Texas State Securities Board.7 In the explainer above, the ochre part of each bar is the simple interest, and the coral part is the extra you get from interest on interest. Watch how the coral part takes over as the years go by.
This is the big one. Because compound growth speeds up over time, the years at the start are worth the most. The Federal Reserve Bank of St. Louis gives this example, at 8% a year with interest added once a year:3
| Saves | Total put in | At age 65 | |
|---|---|---|---|
| Starts at 25 | $5,000 a year for 10 years, then stops | $50,000 | ≈ $787,180 |
| Starts at 35 | $5,000 a year for 30 years | $150,000 | ≈ $611,730 |
The early saver put in a third as much money and still ended up ahead, because her money had ten extra years to compound.3 The Texas State Securities Board shows the same thing another way. Someone who saves $200 a month from age 25 and someone who saves $400 a month from age 45 both put in $96,000. At 6%, the early saver ends up with about $400,290 and the late saver with about $185,740.7
That's why the St. Louis Fed quotes the old saying: "The best time to plant a tree was 20 years ago. The second best time is now."3
All three help, but not equally. Here's $1,000 compounded once a year, worked out with the formula above:6
| Change | Result |
|---|---|
| $1,000 at 5% for 20 years | ≈ $2,653 |
| Double the money: $2,000 at 5% for 20 years | ≈ $5,307 |
| Double the rate: $1,000 at 10% for 20 years | ≈ $6,727 |
| Double the time: $1,000 at 5% for 40 years | ≈ $7,040 |
Doubling the money only doubles the result. Doubling the time does more, because the extra years come at the end, when the snowball is already big. The CFPB lists the ways to grow savings faster: a higher interest rate, adding to your principal, and compounding more often.2
Here's a shortcut you can do in your head: divide 72 by the interest rate. The answer is roughly how many years it takes your money to double.13
| Rate | 72 ÷ rate | Doubles about every… |
|---|---|---|
| 2% | 72 ÷ 2 | 36 years |
| 8% | 72 ÷ 8 | 9 years |
| 9% | 72 ÷ 9 | 8 years |
| 12% | 72 ÷ 12 | 6 years |
The St. Louis Fed's example: $5,000 at 8% doubles about every 9 years, so in 36 years it doubles four times: $10,000, $20,000, $40,000, $80,000. The SEC's calculator gives about $79,840, very close. At 2%, the same $5,000 only reaches about $10,200 in 36 years.3 The rule is an estimate, and it gets less exact at high rates.3
Interest can be added once a year, every month, or even every day. The more often it's added, the sooner your interest starts earning its own interest, so the more you end up with.27 That's why the Texas example's 5% compounded yearly works out to an average of 5.52% a year over five years.7 The effect of compounding more often is real but small next to the rate and the number of years. Certificates of deposit typically pay compound interest.3
Compound interest doesn't care whose side it's on. For borrowers, interest is charged on the unpaid balance plus earlier interest that wasn't paid. The St. Louis Fed notes this is how credit card debt can balloon if it's left unchecked.3
Credit cards state their interest as a yearly rate called the APR (annual percentage rate).4 Those rates are high. In the second quarter of 2026, the average APR on credit card accounts that were charged interest was about 22%, according to the Federal Reserve.5 By the Rule of 72, 72 ÷ 22 ≈ 3.3, so an unpaid balance at that rate would roughly double in just over three years if nothing were paid.
Every number on this page is a math example to show how compounding works. None of it is investment advice. Interest rates on savings change, investment returns aren't guaranteed, and inflation means a dollar in the future buys less than a dollar today. The Federal Reserve aims for 2% inflation over the longer run.3 To try your own numbers, the SEC has a free compound interest calculator,10 and the FDIC's Money Smart for Young People lessons teach how interest on savings is calculated.9
Compound interest shows up all over personal finance. See how it works against you on a card in how credit cards work, why a dollar buys less over time in what causes inflation, and why investment returns go up and down in how the stock market works.
You earn interest on your money, and that interest is added to your balance. Next time, you earn interest on the bigger balance, so you're earning interest on your interest. $100 at 5% a year becomes $105, then $110.25, and the growth speeds up every year.
A lot. The earlier you start, the more years your interest has to earn interest. In a St. Louis Fed example at 8% a year, someone who saves $5,000 a year from 25 to 34 and then stops ends up with about $787,000 at 65. Someone who saves $5,000 a year from 35 to 65, three times as much money, ends up with about $612,000.
A = P(1 + r/n)^(nt), where P is the starting amount, r is the yearly rate as a decimal, n is how many times a year interest is added, and t is the number of years. With interest once a year it becomes A = P(1 + r)^t.
With interest added once a year: $1,000 × 1.06 = $1,060 after year one, then $1,060 × 1.06 = $1,123.60 after year two. That's $3.60 more than simple interest would pay.
It depends on the rate, which is never guaranteed. As a pure math example: at 5% a year compounded yearly it would be about $26,500; at 7%, about $38,700. The Rule of 72 gives a quick check: at 7% money doubles about every 10 years, so roughly twice in 20 years.
There's no magic year, but the curve always starts slow and gets steeper. A handy marker is your doubling time from the Rule of 72 (72 ÷ rate). At 8%, after about three to four doublings (around 33 years), the interest each year becomes bigger than what you first put in.
Both. It helps you when you save, and it works against you when you owe. Unpaid credit card interest is added to your balance and then charged interest too. On most cards, paying the full balance by the due date each month means you pay no interest on purchases.