Compound Interest Calculator: How Money Grows on Itself
Compound interest is how every pension, savings account and long-term investment grows: you earn interest, then next period you earn interest on the interest as well. The growth curve bends upward, slowly at first, then startlingly fast. This compound interest calculator shows you that curve for your own numbers, with or without regular monthly contributions added on top.
If you change one thing after reading this page, change the years. Time sits in the exponent of the formula, so the years end up doing more work than the size of the deposit.
The compound interest formula
- A, the amount you end with.
- P, the starting principal.
- r, the yearly rate as a decimal (7% = 0.07).
- n, how often interest compounds per year (12 = monthly).
- t, the number of years.
Adding a monthly deposit? Each deposit compounds for the months it sits there, and the whole stream adds up to a second amount: deposit × [((1 + i)N − 1) ÷ i], where i is the monthly rate and N the total months. The calculator runs both parts and adds them together.
A worked example, step by step
You invest $10,000 at 7% for 25 years, compounded monthly:
- Monthly rate: 0.07 ÷ 12 = 0.005833. Periods: 12 × 25 = 300.
- Apply the formula: A = 10,000 × (1.005833)300 = $57,254.18. Your money grew by $47,254.18 without you adding a cent, because the interest did the work.
- Now add $200 a month: the deposits themselves total $60,000 over 25 years, but compounded they are worth $162,014.34. Combined ending balance: $219,268.52.
- Notice what happened: you put in $70,000 altogether. You end with $219,268.52. The gap ($149,268.52) is growth, and most of it arrives in the final decade, when the balance is big enough for 7% to mean serious money.
| $10,000 grows to… | 10 years | 20 years | 30 years |
|---|---|---|---|
| at 5% | $16,470 | $27,126 | $44,677 |
| at 7% | $20,097 | $40,387 | $81,165 |
| at 9% | $24,514 | $60,092 | $147,306 |
Read the 7% row slowly: the second decade adds twice what the first did, and the third adds twice again.
How often should interest compound?
More often is better, but the difference isn't as big as the marketing suggests. The same $10,000 at 7% for 25 years ends at $54,274.33 compounded yearly, $57,254.18 monthly, and $57,536.37 daily. Monthly beats yearly by $2,979.85 (real money), but daily adds only $282.19 more. Chasing daily compounding while delaying your start by a year loses far more than it gains. Use the frequency your account actually follows, since the bank's schedule, not your preference, sets the compounding.
The Rule of 72: divide 72 by your yearly rate to estimate how long money takes to double. At 7%, that is about 10.3 years, and the table above agrees: $10,000 becomes $20,097 in ten. At 9% money doubles in 8 years; at 4% it needs 18. Two doublings is 4× your money; three is 8×.
Start at 25 or start at 35? The most expensive decade
Two savers, both putting away $200 a month at 7%. One starts at 25 and stops counting at 65; the other waits ten years and starts at 35. The early starter deposits $96,000 over 40 years and ends with $524,962.68. The late starter deposits $72,000 over 30 years and ends with $243,994.20.
The late starter put in only $24,000 less but finished with $280,968.48 less. The missing money isn't the missing deposits; it's the missing decade of compounding at the end, where the balance is largest. You can't buy back a lost decade later at any price.
Inflation: the silent subtraction
One correction before you quote these numbers at dinner: prices rise too. At 3% yearly inflation, the $57,254.18 from our worked example buys what $27,344.92 buys today. That's still nearly triple your $10,000 in real terms. But cash under a mattress (0% against 3% inflation) loses value every year while feeling perfectly safe, which is why long-term money needs a return that beats inflation, not just a positive one.
A 1% fee sounds tiny
Investment accounts love quoting returns and whispering fees. Take the $200-a-month saver from the worked example, over 25 years. At 7%, the deposits grow to $162,014.34. Now shave one point, a 1% annual fee, or a fund that simply trails the market by that much, and the same deposits at 6% reach $138,598.79. The "tiny" fee consumed $23,415.55, about 14.5% of the ending value, without a single statement ever showing a charge that size. The lump sum fares no better: $10,000 at 6% instead of 7% ends at $44,649.70 rather than $57,254.18, with $12,604.48 surrendered to the same drag. Fees compound exactly the way returns do, in the opposite direction.
The year the interest starts out-earning you
Somewhere inside every long compounding run there's a crossover worth watching for. Track that same $200-a-month plan. In the early years your deposits do nearly all the work, and the interest is a tip on top. But the balance keeps growing, and eventually the interest earned in a single year passes the $2,400 you put in that year. On these numbers it happens in year 11: the account earns $2,580.98 while you deposit your usual $2,400. From then on the money contributes more than you do, every year, by a widening margin. Savers who know the crossover is coming find the dull early years easier to sit through.
Half the deposit, ten more years
One last comparison, because it settles an argument people have with themselves. Saver A puts away $100 a month for 35 years at 7%. Saver B, determined to catch up later, saves $200 a month for 25 years. B deposits $60,000; A deposits just $42,000. Yet A finishes ahead, $180,105.46 against B's $162,014.34, despite handing over $18,000 less. The extra decade beat the doubled deposit, and it did so because A's money spends ten more years in the steep part of the curve. If your budget only stretches to a small deposit, start it now instead of waiting for a bigger one; the extra years matter more than the extra dollars.
Try your own plan at three rates before you trust it: the one you hope for, one a couple of points lower, and one a couple higher. The version that still lands somewhere acceptable at the pessimistic rate is the one worth automating and forgetting about.
Frequently asked questions
What's the difference between APR and APY?
APR is the plain yearly rate. APY is what you effectively earn after compounding is counted, always a little higher. A savings account quoting 7% APR compounded monthly actually yields about 7.23% APY. Compare savings by APY, and loans by APR.
Is it better to invest a lump sum or monthly amounts?
Mathematically, the lump sum wins: every dollar compounds for the full period. In the worked example, $10,000 up front plus $200 a month beats saving the same total and investing it later. But monthly investing wins psychologically: it is automatic, it fits a salary, and it actually happens. The best plan is the one that starts this month.
Does compound interest work against me on debts?
Exactly the same formula, pointed at you. A credit card balance at 24% APR compounded monthly doubles in roughly three years if you only make minimum payments. Compounding is neutral machinery. The side of it you stand on decides whether it feels like magic or a trap, and you're always standing on one side of the formula, so make sure it's the earning side.
How accurate is the Rule of 72?
Close enough for planning: within a few percent for rates between 4% and 12%. It drifts at very high or very low rates. For an exact doubling time, use this calculator and find the year the balance passes twice your start.
What return rate should I assume for investments?
For long-range planning, many people model 5 to 7% for a diversified stock portfolio after inflation, and less for bonds or savings accounts. Nothing's guaranteed (markets move in lumps, not smooth curves), so test your plan at a pessimistic rate too and make sure it still works.
Related calculators: Finance Calculator, Annuity Calculator and Loan Calculator.
Compounding rewards a long runway. Savings, annuities and debt payoff guides continue the theme on the CalcMega Blog.
Estimates only. Real returns vary and are never guaranteed. Nothing here is financial advice.
Further reading: the SEC's own compound interest calculator, from the US Securities and Exchange Commission.