Compound Interest Calculator
Compound interest is interest earning interest. Set a starting balance, a monthly contribution and a rate to see how much of the final figure is money you put in and how much the compounding produced.
Your investment
Contributions are made at the end of each month.
Amounts
Rate and time
Effective annual rate: 7.229%
Growth over time
The gap between the two lines is compound interest doing its work.
Year-by-year breakdown
Interest earned climbs from $919 in year one to $20,061 in year 20.
| Year | Paid in | Interest to date | Balance |
|---|---|---|---|
| 1 | $16,000 | $919 | $16,919 |
| 2 | $22,000 | $2,339 | $24,339 |
| 3 | $28,000 | $4,294 | $32,294 |
| 4 | $34,000 | $6,825 | $40,825 |
| 5 | $40,000 | $9,973 | $49,973 |
| 6 | $46,000 | $13,782 | $59,782 |
| 7 | $52,000 | $18,299 | $70,299 |
| 8 | $58,000 | $23,578 | $81,578 |
| 9 | $64,000 | $29,671 | $93,671 |
| 10 | $70,000 | $36,639 | $106,639 |
| 11 | $76,000 | $44,544 | $120,544 |
| 12 | $82,000 | $53,455 | $135,455 |
| 13 | $88,000 | $63,443 | $151,443 |
| 14 | $94,000 | $74,587 | $168,587 |
| 15 | $100,000 | $86,971 | $186,971 |
| 16 | $106,000 | $100,683 | $206,683 |
| 17 | $112,000 | $115,820 | $227,820 |
| 18 | $118,000 | $132,486 | $250,486 |
| 19 | $124,000 | $150,790 | $274,790 |
| 20 | $130,000 | $170,851 | $300,851 |
What this assumes
- A constant rate of return for the whole period — real markets are far lumpier.
- Contributions are made at the end of each month.
- No tax, account fees or withdrawals are deducted.
Balance after 20 years
$300,851
7.00% compounded monthly, with $500 added each month.
- Total contributions$10,000 initial + $120,000 added
- $130,000
- Total interest earned
- $170,851
- Growth multipleFinal balance ÷ money paid in
- 2.31×
- Effective annual rate
- 7.229%
How compound interest works
Simple interest pays only on your original deposit. Compound interest pays on the deposit and on all the interest already credited, so each period starts from a slightly larger base than the last.
For a lump sum with no contributions the formula is A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate, n the number of compounding periods per year and t the number of years. $10,000 at 10% compounded annually reaches $25,937 after ten years — $15,937 of it interest, and $5,937 of that is interest earned on interest.
Add regular contributions and each one begins compounding from the moment it lands, so early contributions do disproportionate work. That is the whole reason time in the market is talked about more than the size of the deposit.
Why compounding frequency matters (a little)
A 6% rate compounded once a year returns exactly 6%. Compounded monthly it returns 6.168%. Compounded daily, 6.183%. The gain from compounding more often is real but it converges quickly — the jump from annual to monthly is worth far more than the jump from monthly to daily.
This is the difference between a nominal rate and an effective rate. Banks quote APY, which is the effective annual rate with compounding already included, precisely so that accounts with different compounding schedules can be compared directly.
| Compounding | Effective annual rate | Balance after 1 year |
|---|---|---|
| Annually | 6.000% | $10,600.00 |
| Semi-annually | 6.090% | $10,609.00 |
| Quarterly | 6.136% | $10,613.64 |
| Monthly | 6.168% | $10,616.78 |
| Daily | 6.183% | $10,618.31 |
The rule of 72
To estimate how long money takes to double, divide 72 by the annual return. At 6%, roughly twelve years. At 9%, roughly eight. At 12%, six.
It is an approximation that works well between about 4% and 12%, and it is useful precisely because it makes the cost of a lower return obvious. Two percentage points of fees do not reduce your outcome by 2% — over thirty years they can remove a third of it.
What this calculator does not model
A constant return is a modeling convenience, not a forecast. Real returns arrive unevenly, and the order in which good and bad years occur matters a great deal once you start withdrawing money.
Tax is also absent. Interest in a taxable account is generally taxed as ordinary income in the year it is earned, which reduces the amount left to compound. In a tax-deferred or tax-free account it is not, which is a large part of why those accounts perform so differently over decades.
Frequently asked questions
Compound interest is interest calculated on both your original balance and on the interest already added to it. Because each period starts from a larger base than the last, growth accelerates over time. Simple interest, by contrast, is only ever calculated on the original deposit and grows in a straight line.
For a lump sum, A = P(1 + r/n)^(nt), where P is the principal, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. With regular contributions you add the future value of an annuity: PMT × ((1 + i)ⁿ − 1) ÷ i, where i is the rate per contribution period.
Less than most people expect. At a 6% nominal rate, annual compounding returns 6.000% and daily compounding returns 6.183% — a difference of about $18 per $10,000 in the first year. The rate itself and the length of time invested matter far more than how often interest is credited.
A shortcut for estimating doubling time: divide 72 by the annual percentage return. At 6% money doubles in roughly twelve years, at 8% in nine, at 12% in six. It is accurate enough for mental arithmetic in the 4%–12% range and is most useful for seeing how much a small difference in return compounds into over decades.
In a standard taxable account, interest is generally taxed as ordinary income in the year it is credited, whether or not you withdraw it — which reduces the balance left to compound. In tax-deferred accounts such as a traditional 401(k) or IRA, tax is postponed until withdrawal. In a Roth account, qualified withdrawals are not taxed at all. This calculator shows pre-tax growth.