How compound interest works
With simple interest, you earn interest only on what you put in. With compound interest, each period's interest joins the balance, and the next period's interest is calculated on that bigger number. Early on the difference looks small; over decades it's the difference between a savings account and a retirement.
P is your starting balance, r the annual rate as a decimal, n compounding periods per year, and t the number of years. This calculator adds your monthly contributions into the simulation month by month, which is how real accounts behave.
Worked example
$10,000 starting balance, $200/month added, 5% compounded monthly, for 10 years:
The lump sum alone grows to about $16,470. The contributions add $24,000 of deposits which grow to about $31,056. Total: roughly $47,527, of which about $13,527 is interest you never had to deposit.
Start at 25 or start at 35: the $280,000 lesson
The canonical compounding example, run through this calculator: $200/month at 7% (roughly the long-run inflation-adjusted return of US stocks), compounded monthly, until age 65.
| Start age | Years | You deposit | You end with | Growth |
|---|---|---|---|---|
| 25 | 40 | $96,000 | ~$524,963 | ~$428,963 |
| 35 | 30 | $72,000 | ~$243,994 | ~$171,994 |
The ten-year head start costs an extra $24,000 in deposits and finishes about $280,968 ahead. Worse for the late starter: doubling the contribution doesn't close the gap. $400/month for 30 years ends at about $487,988: twice the money in, and still roughly $37,000 behind someone who saved half as much but started at 25. The first decade isn't warming up; it's the highest-paid decade of the whole run, because everything deposited then compounds the longest. Try it against real market history with the S&P 500 investment calculator.
How fast does your money double?
The Rule of 72 (divide 72 by your rate to estimate doubling time in years) is the rare mental shortcut that's genuinely accurate. Here it is against the exact formula, ln(2) ÷ ln(1 + r), with annual compounding:
| Rate | Rule of 72 says | Exact answer |
|---|---|---|
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
You can confirm it above: $10,000 at 8% compounded annually is $19,990.05 after 9 years, a doubling about ten dollars short. The rule is tuned to be nearly perfect around 8% and drifts a little at the extremes. The deeper point is what doubling means in sequence: $10,000 becomes $20,000, then $40,000, then $80,000. Each double adds more than all the growth that came before it, which is why the boring final decade of a long horizon does the heaviest lifting.
Where compound growth actually lives
The rate field in this calculator is doing a lot of work, so anchor it to something real:
High-yield savings accounts have typically paid in the 3% to 5% APY range in recent years, floating up and down with the Fed. FDIC-insured and boring: your balance never goes down, but the rate can, and over long periods it roughly treads water against inflation.
CDs sit in a similar range but lock the rate for a fixed term; the trade is certainty for liquidity, with a penalty if you exit early. Good for money with a known date attached.
Stock index funds have averaged roughly 10% a year over the long run (about 7% after inflation), but "average" hides drops of 30% or more in bad years. The compounding is real; it just shows up over decades, not quarters, which is why this money should be money you won't touch soon.
None of these is a quote (rates change and markets are markets), but they're the honest ranges for choosing what to type into the rate box.
The two levers that matter most
People agonize over compounding frequency, but daily vs. monthly compounding changes the outcome by well under 1%. The levers that actually move the result are time (compounding is exponential: the last 10 years of a 30-year horizon typically generate more interest than the first 20 combined) and rate. That's why starting early beats starting big: $200/month from age 25 usually out-grows $400/month from age 40.
When you have a target number instead of a timeline, the money goal calculator inverts this math and tells you the monthly saving a goal requires; the time value of money calculator solves for any missing variable; and when it's finally time to spend the pile, the retirement withdrawal calculator runs this whole machine in reverse.