Compound interest calculator
Project your savings with regular contributions and see how much of the result is interest rather than your own money.
Advanced options
Final balance
$124,379.03
Contributed
$53,000.00
Interest
$71,379.03
At this rate, money doubles every 10.2 years.
See the year-by-year breakdown
| Year | Contributed | Interest | Total |
|---|---|---|---|
| 1 | $7,400.00 | $439.97 | $7,839.97 |
| 2 | $9,800.00 | $1,085.24 | $10,885.24 |
| 3 | $12,200.00 | $1,950.65 | $14,150.65 |
| 4 | $14,600.00 | $3,052.12 | $17,652.12 |
| 5 | $17,000.00 | $4,406.71 | $21,406.71 |
| 6 | $19,400.00 | $6,032.72 | $25,432.72 |
| 7 | $21,800.00 | $7,949.77 | $29,749.77 |
| 8 | $24,200.00 | $10,178.90 | $34,378.90 |
| 9 | $26,600.00 | $12,742.67 | $39,342.67 |
| 10 | $29,000.00 | $15,665.27 | $44,665.27 |
| 11 | $31,400.00 | $18,972.64 | $50,372.64 |
| 12 | $33,800.00 | $22,692.60 | $56,492.60 |
| 13 | $36,200.00 | $26,854.97 | $63,054.97 |
| 14 | $38,600.00 | $31,491.74 | $70,091.74 |
| 15 | $41,000.00 | $36,637.19 | $77,637.19 |
| 16 | $43,400.00 | $42,328.11 | $85,728.11 |
| 17 | $45,800.00 | $48,603.92 | $94,403.92 |
| 18 | $48,200.00 | $55,506.90 | $103,706.90 |
| 19 | $50,600.00 | $63,082.40 | $113,682.40 |
| 20 | $53,000.00 | $71,379.03 | $124,379.03 |
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Compound interest is the effect of one period's interest earning interest of its own in the next. Over short horizons it barely shows; over twenty or thirty years it becomes the single biggest driver of the final number — bigger even than how much you put in each month.
This calculator separates the two halves of the balance explicitly: the money you put in, and the money the interest produced. That separation is what makes visible the point where interest overtakes contributions, which is usually when savings start to move on their own.
How to use it
- 1
Enter the starting amount and contribution
The starting amount is what you already have saved. The contribution is what you add regularly; leave it at zero if you are not adding anything.
- 2
Use a realistic annual rate
A bank deposit usually sits between 1% and 3%. The long-run historical return of a broad stock index, before tax, is around 7% nominal. Treat figures well above that with scepticism.
- 3
Adjust the advanced options if needed
Compounding frequency changes the result: the same nominal rate compounded daily returns slightly more than compounded once a year. Adding inflation also shows what the balance is worth in today's money.
- 4
Read the chart and the table
Hover the chart to see the breakdown for any year, and use the buttons above it to read the same projection four ways: the area for the shape of the growth, the lines for the two trajectories without the fills in the way, the bars for what each individual year added, and the split for what the final pile is actually made of. The year-by-year table gives the same exact figures, handy for copying into a spreadsheet.
Things worth keeping in mind
What to check before trusting a projection
A thirty-year projection is a scenario, not a forecast. These are the assumptions that distort it most:
- Constant returns: real markets have negative years, and the order they arrive in matters if you are withdrawing.
- Fees: a 1% annual fee against a 7% return takes close to a quarter of the final balance over 30 years.
- Tax: not included, and it depends on your country and product.
- Inflation: without adjusting for it, the final figure looks larger than it is worth.
When interest overtakes contributions
On the chart, that moment is when the interest band grows thicker than the contributions band. At 7% a year with steady monthly contributions it usually happens between year 15 and year 20.
It is the strongest argument for starting early even with small amounts: the first years add little balance, but they are the ones buying compounding time for everything that comes after.
Four thousand years of the same calculation
Compound interest is older than algebra. Babylonian clay tablets written some 3,800 years ago pose problems of exactly this shape: if silver is lent at 20% a year, how long until it doubles? The scribe worked it out from tables of successive powers plus linear interpolation, and landed on a little over three years and eight months — the right answer with the tools of the day.
The mental shortcut people still use is a Renaissance one. Luca Pacioli wrote it down in 1494 in his "Summa de arithmetica": divide 72 by the interest rate and you get the years it takes the capital to double. Pacioli never explained where the 72 came from; the derivation, with logarithms, arrived a century and a half later.
The first book devoted entirely to compound interest was published in London in 1613 by the mathematician Richard Witt: "Arithmeticall Questions", with tables computed to eight decimal places, every one of them by hand. And in 1683 Jacob Bernoulli asked what would happen if interest were compounded not yearly or monthly but continuously. The answer to that question is the number e, 2.71828…, which entered the world as a compound-interest problem before it was a mathematical constant.
- 20%
- The standard annual rate on silver loans in ancient Babylon.
- 1494
- The year Pacioli published the rule of 72 in his "Summa de arithmetica".
- e = 2.71828…
- The constant Bernoulli found in 1683 by asking what happens when interest compounds every instant.
Where the number comes from
Compound interest is interest calculated on interest already earned. The formula is A = P(1 + r/n)^(n·t): the starting principal P multiplied by one plus the annual rate r divided by the number of compounding periods per year n, all raised to those periods times the years t.
The exponent does the work, not the rate. Seven per cent a year for 10 years is not 70%: it is 96.7%, because each year the percentage applies to a bigger base. Over 30 years that same 7% multiplies the capital by 7.6. The curve is flat for years and then takes off, which is why starting early matters more than contributing heavily.
Compounding frequency matters less than people expect. Moving from annual to monthly compounding at 6% raises the real return from 6% to 6.17%; moving to daily leaves it at 6.18%. There is a ceiling: compounding infinitely often converges on e raised to r, which is precisely where the number e came from.
That distinction has a legal name. The nominal rate is the advertised one; the effective rate — APY in the United States, AER in the UK — includes the effect of compounding, and it is the only one you can use to compare two products. When a bank prints the nominal rate large and the effective rate small, the gap between them is exactly what it would rather you did not compare.
Estimating it in your head: the rule of 72
You do not need a calculator to know whether an offer is worth reading twice. This gets you the order of magnitude in five seconds.
- 1
At 6% a year: 72 ÷ 6 = 12. That is how many years the money takes to double. At 9%, eight years. At 3%, twenty-four.
- 2
Investing for 30 years at 6% fits two and a half doublings (30 ÷ 12). Two doublings is ×4, and the remaining half adds roughly another ×1.4.
- 3
$10,000 at 6% for 30 years: ×4 gives 40,000, and the half doubling brings it to about 57,000. The exact answer is 57,435, so the error is under 1%.
- 4
If something promises to double your money in 4 years, the implied rate is 72 ÷ 4 = 18% a year. When that number lands far above what the market pays, you know what kind of product you are looking at.
- 5
The rule is most accurate between 4% and 12%. Below 3% it understates the wait, and above 20% it drifts badly: at 30%, 72 ÷ 30 gives 2.4 years when the true answer is 2.64.
Things worth knowing
The rule of 72 is over 500 years old
It appears in print in 1494, in Luca Pacioli’s Summa de Arithmetica — the same book that documented double-entry bookkeeping. Pacioli states it as common knowledge and never proves it, so merchants were clearly already using it.
The number e was born from this question
In 1683 Jacob Bernoulli asked what would happen if interest compounded infinitely often within a year. The answer converged on 2.71828…, the constant now named after Euler that underpins half of mathematics.
Einstein never said it
The line about compound interest being "the eighth wonder of the world" is attributed to him everywhere and has no source behind it: it appears in none of his writing, and in no publication before the 1980s.
The doubling penny
A penny that doubles every day for 30 days ends at $5,368,709. On day 29 you have half of that: more than half the total arrives in the final doubling, which is exactly what makes exponential growth so hard to feel.
A nominal rate and an effective rate are different animals
A 24% nominal rate compounded monthly is 26.8% effective. On a credit card that gap is almost three points that never appear in the big number on the advert.
Frequently asked questions
What is the compound interest formula?
For a lump sum with no contributions, the final balance is P × (1 + r/n)^(n×t), where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year and t the years. With regular contributions you must also add the future value of each contribution, which is what this calculator does month by month.
Why does the result change when I alter the compounding frequency?
Because interest joins the principal sooner and starts earning interest itself. At 6% nominal over ten years, compounding daily produces roughly 3% more final balance than compounding once a year.
What difference does contributing at the start or end of the period make?
Contributing at the start gives every contribution one extra period of growth. With monthly contributions the difference is small over one year, but over thirty years it works out to around 5% more final balance.
Should I enter the rate before or after tax?
The calculator applies no tax. For a net projection, enter the return you expect after whatever tax applies to you; in many countries savings returns are taxed on withdrawal rather than every year.
What does the inflation field do?
It discounts the final balance back to today's money. A balance of 100,000 in 30 years' time with 2% annual inflation buys roughly what 55,000 buys today. It does not change the projection, only restates it in current purchasing power.
Is the rule of 72 reliable?
As a mental shortcut, yes: dividing 72 by the interest rate gives the years it takes money to double. It is fairly accurate between 4% and 12%. The figure this tool shows is the exact calculation, not the approximation.
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