You have been told a number. Somewhere in your reading it said ten percent a year, and the sentence attached to it promised a fortune, and neither the number nor the promise came with a table. I have taught high-school mathematics for thirty-five years, and the half-life of a growth claim without a table is about as long as it takes a student to forget it. So nothing on this page gets asserted that is not in a row: the starting amount, the rate, the years, and what the money comes to. Four rates — 10 percent, 7 percent, 4 percent, 0 percent — one stake of $10,000, thirty years, every cell counted. That is the whole article.
The rate labels carry dates, because the arithmetic below is exact and only the rates are assumptions. Where each of the four numbers came from, and the date on it, is a table of its own, and it comes first.
The Three Questions, Answered Before the Math
What is compound interest? Interest that starts earning interest. You put $10,000 at 7 percent and the first year pays $700; the second year pays 7 percent on $10,700, which is $749 — because the $700 you already earned stays in the room and works. That is the entire mechanism. The table after it is what the mechanism does over thirty years.
What is the difference between simple and compound interest? Simple pays the rate on your money only: at 7 percent for thirty years, $2,100 a year, forever, ending at $31,000. Compound pays it on your money and on everything it has already earned, and on this same stake it ends at $76,123. There is a row below for each rate that shows the gap; at 7 percent the gap is $45,123, which is more than twice all the simple interest in the thirty years.
What is a compound interest calculator? The four lines under “The Formula, Shown,” below, with text boxes bolted on. Mine is on this page and runs any rate, any number of years, any starting amount, and any yearly contribution — and the printed tables next to it are the same arithmetic done on paper, so a browser without JavaScript still gets the whole answer.
The Four Rates, Dated
A rate on this page is a fact with a date, not a mood. Here is where each of the four came from.
| Rate | What it was in 2026 | Where the number comes from |
|---|---|---|
| 10% | The market’s own row, in dollars. The S&P 500 with dividends reinvested compounded 10.02% a year from the start of 1928 through the end of 2025: $100 became $1,157,598.95 | Damodaran (NYU Stern), Historical Returns on Stocks, Bonds and Bills, page updated January 5, 2026 |
| 7% | The market row minus the price line, rounded. Ten percent nominal against the price line leaves roughly 6.4 to 6.8 percent of real growth depending on the window; 7 percent is the top of that wedge, the number the planning tables print | The same 1928–2025 return, against the Bureau of Labor Statistics CPI-U, which compounded 3.44% a year across 1948–2024 |
| 4% | The near-cash row. A Treasury bill, the safest thing that pays a rate at all, compounded 3.37% a year across the whole 1928–2025 record — and in October 2026 pays more than its own record: the 3-month bill yielded 4.19% on October 2, 2026, and the 10-year note 5.28% | Same Damodaran series for the record; the U.S. Treasury daily yield curve for the 2026 quotes, fetched October 4, 2026 |
| 0% | Not a market rate. The rate on money that earns nothing — cash in a drawer, the untouched bank balance, the money that never got a job. The counterweight is the price line: CPI-U rose 3.4% in the twelve months to August 2026 | Bureau of Labor Statistics CPI-U via FRED (series CPIAUCSL), fetched October 4, 2026; the same 3.4% print this site’s retirement calculator dates and indexes with |
One more line on the 7 percent, because this site does not keep one number in its pocket: the calculator on the retirement number plans at 6 percent real, and it says so on its own dated page. Six and seven are the same record read against two different price windows — the wedge is which window you subtract, not which site you trust — and this page runs the higher one and labels it.
Three dates to keep hold of. The market record runs 1928–2025 and was republished January 5, 2026; the price print is the twelve months to August 2026; the cash quotes are October 2, 2026. When those sources publish, these labels move. No rate on this page is a forecast. A table is not a prediction; it is arithmetic done honestly.
The Formula, Shown
Four lines. If you can read them, you can run the calculator by hand on a napkin, and you can check any box that claims to be one.
start with the starting amount
for each year:
balance = balance x (1 + rate) + yearly contribution
read the last row
Rounding, stated once: the balance carries all its decimals through the thirty years and is rounded once, at the end, to the dollar. The yearly contribution lands at the end of each year, so it earns nothing in the year it arrives — the conservative end of the convention, and the reason my numbers can print a dollar lower than a box that assumes your money arrives on New Year’s Day. And one warning worth more than the rest of this section: a monthly contribution at twelve times a year is not a yearly contribution. It arrives earlier on average, so it finishes ahead by a few percent. Run the box with the contribution set the way the box defines it.
The Calculator
The compound table — the four formula lines above, running
The default is the stake the printed tables below use: $10,000.
Lands at the end of each year. For $200 a month, enter $2,400 — and note the box is a little conservative against a monthly schedule.
Dated October 2026: 10 = the market's 1928–2025 record. 7 = the market less the price line. 4 = what bills paid on October 2, 2026. 0 = money that earns nothing.
Dated: 3.4% = CPI-U over the twelve months to August 2026. It changes no balance above it; it only restates what the balance buys.
—
—
The box runs exactly the four lines above, with the contribution at the end of each year and one rounding at the finish. It does not model taxes, fees, or the fact that real markets do not deliver one rate every year — the table is what the rate does, not what the market promises.
The box is the formula with a text field on each input. If it renders as an empty frame in an old browser, nothing is lost that the printed tables below do not already carry.
The Matrix: $10,000, Thirty Years, Four Rates
One stake. Four rates. Thirty years. The rates are the dated labels from the table above, and the last column is the one I would read first. Every cell comes from one line of arithmetic — $10,000 × (1 + rate)^years — and any cell can be checked in the ten seconds it takes to punch it.
| Rate | Year 1 | Year 5 | Year 10 | Year 15 | Year 20 | Year 25 | Year 30 |
|---|---|---|---|---|---|---|---|
| 10% | $11,000 | $16,105 | $25,937 | $41,772 | $67,275 | $108,347 | $174,494 |
| 7% | $10,700 | $14,026 | $19,672 | $27,590 | $38,697 | $54,274 | $76,123 |
| 4% | $10,400 | $12,167 | $14,802 | $18,009 | $21,911 | $26,658 | $32,434 |
| 0% | $10,000 | $10,000 | $10,000 | $10,000 | $10,000 | $10,000 | $10,000 |
The table is in five-year steps because thirty columns is a wall; the calculator above runs any year between, and the year that matters to you is usually not a multiple of five.
Now read the last column. Thirty years at 10 percent turns $10,000 into $174,494 — that is 17.4 times the money. At 7 percent: $76,123, or 7.6 times. At 4 percent: $32,434, or 3.2 times. At 0 percent: $10,000, which is not a rounding error, it is the point.
And look at the gaps in that final column, because they are the argument.
- 10% against 7%: $98,371. A three-point difference in the rate, and over thirty years it is worth more than the entire 4% row.
- 7% against 4%: $43,689. The same three points, lower down the scale, buy less than half as much. The same rate difference is not the same money; it is worth more when the base is bigger.
- 4% against 0%: $22,434. Four points, and thirty years, and it is worth slightly more than twice the original stake.
Here is what I want a young reader to see. At 7 percent, the first year of growth is $700. The thirtieth year of growth is $4,980 — seven times the first year, from the same money doing the same thing, and the only variable that changed was the number of years. A rate is small and steady; time is large and it does not stop. Time is the variable the money never is.
The 0% Row: The Rate That Runs Backward
The 0% row is the one most tables leave out, because a table about money likes to show money growing. But the 0% row is not a hypothetical — it is where a great deal of the world’s money actually sits, and it is the only row here that describes the cash in a drawer exactly.
Watch it. Over thirty years the balance is $10,000 in every single cell. It never moves. Meanwhile the price line from the dated table above — CPI-U, 3.4% over the twelve months to August 2026 — does not stand still next to it. At that rate, restated in what a dollar buys today:
| Money parked at 0% | Nominal balance | What it still buys, in 2026 goods |
|---|---|---|
| After 10 years | $10,000 | about $7,158 |
| After 20 years | $10,000 | about $5,124 |
| After 30 years | $10,000 | about $3,668 |
Ten thousand dollars under a mattress for thirty years is a loss of two-thirds, and it is a loss that happens entirely without any number appearing on the balance. At 3.4 percent, the buying power of a parked $10,000 halves in about twenty-one years. The 0% row is not “safe.” It is the only row on this page that guarantees a loss, and it guarantees it precisely because nothing on the statement moves.
The same restatement applied to the 7% row is worth seeing once: $76,123 of nominal thirty-year money, divided by the price line, buys about $27,919 of 2026 goods. The number is still large. It is 2.8 times the money, not 7.6. When anyone quotes you a growth figure, the second question is in what year’s dollars — and if they have not thought about it, you have just learned something about the rest of their arithmetic too.
The Row That Surprises: Started Sooner
This is the comparison I have made on the back of every envelope I could find, and readers do not believe it until they see the row. Two people. Both stop at 65. One starts at 25 and puts in $1,200 a year for forty years — $48,000 out of pocket, total. The other starts at 35, has a better salary, and puts in $2,400 a year for thirty years — $72,000 out of pocket, twice the annual effort and half again the total.
| Rate | Started at 25: $1,200/yr, 40 yrs ($48,000 in) | Started at 35: $2,400/yr, 30 yrs ($72,000 in) | The last column says |
|---|---|---|---|
| 4% | $114,031 | $134,604 | the earlier start loses by $20,573 |
| 7% | $239,562 | $226,706 | the earlier start wins by $12,856, having contributed $24,000 less |
| 10% | $531,111 | $394,786 | the earlier start wins by $136,325, having contributed $24,000 less |
Read the 7% line first, because it is the modest one, and the modest one is the interesting one. The person who put in half the money every year, ten years earlier, finishes ahead. Not by a whisker, and not because of a clever fund — I have not picked a fund, a portfolio, or even a decade, only a rate that has an exact definition and a date. The person who saved twice as hard, later, is still behind, and the money they are behind by came out of ten years of the other person’s calendar.
Now read the whole table, including the row that goes the other way, because I am not going to fold it. At 4 percent the earlier start loses — the thirty-year double contributes half again the money and finishes $20,573 ahead. The head start is not magic; it is arithmetic, and the arithmetic turns over at a particular rate. Set the two totals equal — $1,200 for forty years against $2,400 for thirty — and the balance point is 6.28 percent a year: at that rate the two finish level, about $199,500 each. Below it, money matters more than the calendar. Above it, the calendar wins, and it wins by more the further up you go — $12,856 at 7 percent, $136,325 at 10.
So the honest form of the claim, which is also the more useful one: the smaller number, started sooner, wins — when the rate clears about 6.3 percent. The dated set at the top of this page says the market cleared it across the whole record — 10.02 percent nominal from 1928 through 2025, and roughly 6.4 to 6.8 percent real depending on which price window you subtract, still above the turn, though with less room to spare. Cash never cleared it: the bill’s whole-record 3.37 percent, and even the 4.19 percent it paid on October 2, 2026, sit below 6.3. Which row your money is actually in is your decision, and it is the decision — the table above only prices each one. You will not believe it yet. Put your own two ages in the calculator, use the same rate twice, and watch which line comes out on top. That is the experiment, and it takes about forty seconds.
Simple Against Compound
One row per rate, and the question is answered. Simple interest pays the rate on your money, never on what your money has earned. Compound pays it on both. Same $10,000, same thirty years.
| Rate | Simple: $10,000 × (1 + 30 × rate) | Compound: $10,000 × (1 + rate)³⁰ | The gap |
|---|---|---|---|
| 10% | $40,000 | $174,494 | $134,494 — the compound total is 4.4 times the simple one |
| 7% | $31,000 | $76,123 | $45,123 — more than twice all the simple interest |
| 4% | $22,000 | $32,434 | $10,434 |
At 7 percent, simple interest earns $21,000 across the thirty years. The compounding — the earnings on the earnings, nothing else — earns $45,123. The bonus is larger than the entire salary. At 4 percent the whole thirty years of simple interest add $12,000 — a quarter more than the same stake’s entire first decade at 7 percent adds ($9,672), which is what thirty sedate years can do against ten ambitious ones. Whatever else you take from this page, take the shape of it: simple interest is a straight line, and compounding is a curve that spends its first ten years being boring.
What the Rows Do Not Say
Four things the tables above cannot tell you, and I will not pretend otherwise.
The market does not deliver one rate a year. The 10% row is what the S&P 500 averaged across 1928–2025 in dollars — and inside that record are years like −43.8% (1931) and +52.6% (1954). The row is the destination of the average; the route had both of those years in it, and your money has to stay in the room through years like that to collect the average. The math on this page is exact. The rate is history.
A rate is not a vehicle. Nothing here picks a fund, a portfolio, or an allocation — that is not this lane, and the tables would not change if you swapped vehicles, because what changes is the cost the vehicle carries, not the compounding. The site counts that separately, and it is worth reading: Index Fund vs ETF in 2026: The Real Cost Gap runs the same kind of arithmetic on fees, and a fee is simply a negative rate on a table you are not shown.
A rate is not a goal. This page counts money growing. It does not count what the money is for — the number you would need, or what you can spend from it once you have it — and it does not pretend to. Those are counted, with their own dated assumptions, in How Much Do You Need to Retire? and in the retirement calculator behind the site’s retirement number.
The rows say nothing about your life. They assume the money stays put and the contributions land at the end of each year, thirty years running. That is the only assumption in the arithmetic, and it is the one readers break.
Where the Money in the Table Comes From
If the arithmetic is going to run for thirty years, the first dollar has to survive the first month, and that is a different table. The reserve that keeps a bad Tuesday from interrupting the compounding is sized and dated in the emergency fund calculator next door; the arithmetic for getting out from under the debt that eats a contribution is in the debt payoff calculator. And for the first dollar itself, before any of these rates have anything to work on: the first $500 to invest, in 2026. The rates on this page are what money does after it starts; those pages are about starting.
The table has been doing the explaining all along. $10,000 at 7 percent for thirty years is $76,123, and the difference between 7 percent and 0 percent is not a number in a lecture — it is $66,123 on one stake of $10,000 — and at every rate above 6.3 percent, a head start beating twice the contribution. Run your own rows. Read the last column — it is the only column that knows how many years you had.