Article · Money
Compound interest calculator
Compound interest is interest on interest: what a sum earns is added to it and earns too, so the growth speeds up the longer it runs. At 7% a year money doubles about every 10.2 years — and from January 1960 to October 2026, $1,000 in US stocks with dividends reinvested grew to $848K; in cash at the fed funds rate, to $25.4K.
Year by year
| Year | Put in so far | Interest so far | Interest that year | Balance |
|---|---|---|---|---|
| 1 | $11,200 | $762 | $762 | $11,962 |
| 2 | $12,400 | $1,666 | $904 | $14,066 |
| 3 | $13,600 | $2,722 | $1,056 | $16,322 |
| 4 | $14,800 | $3,941 | $1,219 | $18,741 |
| 5 | $16,000 | $5,336 | $1,394 | $21,336 |
| 6 | $17,200 | $6,917 | $1,582 | $24,117 |
| 7 | $18,400 | $8,700 | $1,783 | $27,100 |
| 8 | $19,600 | $10,698 | $1,998 | $30,298 |
| 9 | $20,800 | $12,928 | $2,230 | $33,728 |
| 10 | $22,000 | $15,405 | $2,477 | $37,405 |
| 11 | $23,200 | $18,148 | $2,743 | $41,348 |
| 12 | $24,400 | $21,177 | $3,028 | $45,577 |
| 13 | $25,600 | $24,511 | $3,334 | $50,111 |
| 14 | $26,800 | $28,172 | $3,662 | $54,972 |
| 15 | $28,000 | $32,186 | $4,013 | $60,186 |
| 16 | $29,200 | $36,576 | $4,390 | $65,776 |
| 17 | $30,400 | $41,370 | $4,794 | $71,770 |
| 18 | $31,600 | $46,597 | $5,228 | $78,197 |
| 19 | $32,800 | $52,290 | $5,692 | $85,090 |
| 20 | $34,000 | $58,480 | $6,190 | $92,480 |
| 21 | $35,200 | $65,205 | $6,725 | $100,405 |
| 22 | $36,400 | $72,502 | $7,298 | $108,902 |
| 23 | $37,600 | $80,414 | $7,912 | $118,014 |
| 24 | $38,800 | $88,985 | $8,571 | $127,785 |
| 25 | $40,000 | $98,261 | $9,277 | $138,261 |
| 26 | $41,200 | $108,296 | $10,034 | $149,496 |
| 27 | $42,400 | $119,142 | $10,846 | $161,542 |
| 28 | $43,600 | $130,859 | $11,717 | $174,459 |
| 29 | $44,800 | $143,510 | $12,651 | $188,310 |
| 30 | $46,000 | $157,162 | $13,652 | $203,162 |
10.6% a year with dividends reinvested, doubling every 6.9 years; after inflation $74K
7.4% a year; after inflation $10.2K
5.8% a year, coupons reinvested; after inflation $3,650
5.0% a year; after inflation $2,218: cash stayed ahead of prices by 1.2% a year
$1,000 of January 1960 bought what $11.5K buys in October 2026: 3.7% a year, doubling every 19 years
What is compound interest?
With simple interest you earn on the sum you put in, and only on it. With compound interest each period's interest joins the sum and earns interest itself, so every year's interest is bigger than the last. Take $1,000 at 10% a year: in the first year both kinds pay $100.
After that they part. Simple interest keeps paying $100 a year and leaves you $4,000 after 30 years. Compound interest pays $1,586 in year 30 alone and leaves you $17,449 — 17.4 times the money you started with.
The formula, and how often interest is added
A sum P at a yearly rate r, credited n times a year for t years, grows to:
A = P × (1 + r/n)n·t
Written as a fraction, 7% is 0.07: $10,000 credited monthly for 30 years becomes $81,165. Monthly additions add a second part, each addition growing from its own month; the calculator above does that month by month.
How often interest is credited matters less than people think. For $10,000 at 7% over 30 years, monthly instead of yearly crediting adds $5,042; daily instead of monthly only $480. The rate itself matters far more.
| Interest credited | After 30 years | Interest | Effective rate a year (APY) | More than yearly |
|---|---|---|---|---|
| Yearly | $76,123 | $66,123 | 7.00% | — |
| Twice a year | $78,781 | $68,781 | 7.12% | +$2,658 |
| Quarterly | $80,192 | $70,192 | 7.19% | +$4,069 |
| Monthly | $81,165 | $71,165 | 7.23% | +$5,042 |
| Daily | $81,645 | $71,645 | 7.25% | +$5,523 |
| Continuously | $81,662 | $71,662 | 7.25% | +$5,539 |
The rule of 72
To see how long money takes to double, divide 72 by the yearly rate: at 7% that gives 10.3 years, against an exact 10.2. The rule is exact at about 7.8% and stays close from 1% to 15%: at 1% it says 72 against an exact 69.7, at 15% 4.8 against 5.0. For interest added continuously the exact number is 69.3, which is why some use a rule of 70.
In the picture each brick is one doubling. Over 50 years, 3% a year turns $1 into $4.38, 10% into $117 and 15% into $1,084. The ticks show where the rule of 72 puts each doubling; by the last bricks its small error adds up.
The rule of 72 against the exact answer
| Rate a year | 72 ÷ rate, years | Exact, years | Rule's error | Growth in 50 years |
|---|---|---|---|---|
| 1% | 72.0 | 69.7 | +3.4% | ×1.64 |
| 2% | 36.0 | 35.0 | +2.8% | ×2.69 |
| 3% | 24.0 | 23.4 | +2.3% | ×4.38 |
| 4% | 18.0 | 17.7 | +1.9% | ×7.11 |
| 5% | 14.4 | 14.2 | +1.4% | ×11.5 |
| 6% | 12.0 | 11.9 | +0.9% | ×18.4 |
| 7% | 10.3 | 10.2 | +0.4% | ×29.5 |
| 8% | 9.0 | 9.0 | −0.1% | ×46.9 |
| 9% | 8.0 | 8.0 | −0.5% | ×74.4 |
| 10% | 7.2 | 7.3 | −1.0% | ×117 |
| 11% | 6.5 | 6.6 | −1.5% | ×185 |
| 12% | 6.0 | 6.1 | −1.9% | ×289 |
| 13% | 5.5 | 5.7 | −2.3% | ×451 |
| 14% | 5.1 | 5.3 | −2.8% | ×700 |
| 15% | 4.8 | 5.0 | −3.2% | ×1,084 |
What real money compounded at since 1960
Calculators assume one rate for ever; real assets never pay one. Here is $1,000 put in January 1960 into US stocks (the S&P 500, dividends reinvested), 10-year US Treasury bonds (coupons reinvested), gold, and cash earning the federal funds rate. In October 2026 the stocks were worth $848K (10.6% a year), gold $116K (7.4%), bonds $41.8K (5.8%) and cash $25.4K (5.0%).
The winner depends on the start year: stocks from 1960, 1970, 1980, 1990 and 2010; gold from 2000. Pick a start above the chart to watch the race from there.
Inflation compounds too: prices rose 11.5 times over the same years, 3.7% a year, doubling about every 19 years. After inflation $1,000 in stocks grew to $74K of 1960 buying power, in gold to $10.2K, in bonds to $3,650 and in cash to $2,218: cash stayed ahead of prices by 1.2% a year.
| Put in | US stocks | 10-year Treasuries | Gold | Cash (fed funds) | Prices (CPI) |
|---|---|---|---|---|---|
| January 1960 | $848K+10.6% a year | $41.8K+5.8% a year | $116K+7.4% a year | $25.4K+5.0% a year | ×11.5+3.7% a year |
| January 1970 | $398K+11.1% a year | $33K+6.4% a year | $117K+8.8% a year | $16.6K+5.1% a year | ×8.88+3.9% a year |
| January 1980 | $217K+12.2% a year | $19K+6.5% a year | $6,079+3.9% a year | $8,049+4.6% a year | ×4.32+3.2% a year |
| January 1990 | $46.6K+11.0% a year | $5,720+4.9% a year | $10K+6.5% a year | $2,937+3.0% a year | ×2.64+2.7% a year |
| January 2000 | $8,720+8.4% a year | $2,659+3.7% a year | $14.4K+10.5% a year | $1,745+2.1% a year | ×1.99+2.6% a year |
| January 2010 | $9,242+14.2% a year | $1,373+1.9% a year | $3,672+8.1% a year | $1,296+1.6% a year | ×1.55+2.6% a year |
Cash is the effective federal funds rate compounded every day: close to what Treasury bills and money market funds paid; bank deposits often paid less. Gold has one price a year in 1960–1967, and its official price was fixed until 1971. No taxes or fees anywhere. Cash: Federal Reserve Board, H.15 (effective federal funds rate)
The EFFR is subject to the Terms of Use posted at newyorkfed.org. The New York Fed is not responsible for publication of the EFFR by BigCapital, does not sanction or endorse any particular republication, and has no liability for your use.
Questions people ask
What is compound interest?
Interest on interest: each period's interest is added to the sum and earns interest from then on. $1,000 at 10% a year becomes $4,000 in 30 years with simple interest and $17,449 with compound interest.
How do you calculate compound interest?
Multiply the sum by (1 + r/n) to the power n·t, where r is the yearly rate as a fraction, n how many times a year interest is credited and t the years: $10,000 × (1 + 0.07/12)12·30 = $81,165. With regular additions, add up every addition grown the same way from its own month — or use the calculator above.
What is the rule of 72?
A shortcut for doubling time: 72 divided by the yearly rate is roughly the number of years money takes to double. At 7%, 10.3 years (exact: 10.2). It is most accurate near 7.8% and off by no more than 3% between 1% and 15%.
How much will $10,000 be worth in 30 years?
At 7% a year credited monthly, $81,165; at 4%, $33,135; at 10%, $198,374 — with nothing added. Adding $100 a month at 7% gives $203,162.
Is daily compounding better than monthly?
Slightly. $10,000 at 7% for 30 years grows to $81,165 credited monthly and to $81,645 credited daily — $480 more; even continuous crediting gives only $81,662. Compare effective yearly rates (APY) rather than how often interest is credited.
Go deeper
How the numbers are calculated
- Calculator: interest is credited n times a year; between credits money grows at the same effective rate, so a sum left alone grows exactly by (1 + r/n)n·t. Additions come at the end of each month and earn from the next month. No taxes or fees. “After inflation” divides by 2.5% a year, the US consumer price inflation of the last 30 years (October 1996 to October 2026).
- Stocks: the S&P 500 (before 1957 its predecessors) with dividends reinvested every month; bonds: a constant-maturity 10-year US Treasury bond, coupons reinvested (Shiller's method); US consumer prices — Robert J. Shiller, Online Data (Yale University).
- Gold: World Bank Commodity Price Data (The Pink Sheet), monthly average price in US dollars, CC BY 4.0.
- Cash: the effective federal funds rate, daily since July 1954, Board of Governors of the Federal Reserve System (H.15); compounded every calendar day on an actual/360 basis, then averaged by month.
- Values are monthly averages (bonds: Shiller's monthly total return); the race starts in January of the chosen year and ends in Oct 2026. Compound rate a year = (end ÷ start)12 / months − 1.
- After inflation: values divided by the US consumer price index of their month, so they are in dollars of the start month.
- Shiller's notes on the latest months: Oct price is Oct 2nd close; Sept/Oct CPI estimated; Oct GS10 is Oct 2nd value.
- Past returns are history, not a forecast, and a calculator is arithmetic, not a promise. Nothing here is investment advice.