How compound interest grows your money
Each month the calculator multiplies your balance by (1 + r), where r is the monthly rate that adds up to your yearly return over twelve months, and then adds your deposit. The interest you earn in one month is included in the balance that earns interest the next month. Over long periods this snowball effect is larger than the deposits themselves.
In the chart, the blue part of each bar is money you put in and the green part is growth. Look at how the green section takes over in later years, even though your monthly deposit stays the same.
The formula, and what every variable means
future value = S × (1 + r)n + D × ((1 + r)n − 1) ÷ r
| Symbol | Meaning | How it is found |
|---|---|---|
| S | Starting balance | The amount you already have |
| D | Monthly deposit | What you add at the end of each month |
| r | Monthly rate | (1 + annual return ÷ 100)1/12 − 1 (7% becomes 0.005654), so twelve months of growth give exactly the yearly return |
| n | Number of months | Years × 12 |
The first term is your starting balance growing on its own. The second is the total of all deposits, each growing for the time it is invested. If you raise your deposit each year, the calculator applies the same idea one year at a time.
Worked example 1, by hand: $5,000 plus $300 a month at 7% for 20 years
- Monthly rate: r = (1 + 7 ÷ 100)1/12 − 1 = 0.005654. Check: (1 + r)12 = 1.0700, which is the yearly 7%. And n = 20 × 12 = 240.
- Growth factor: (1 + r)240 ≈ 3.8697.
- Starting balance grown: $5,000 × 3.8697 = $19,348.
- Deposits grown: $300 × (3.8697 − 1) ÷ 0.005654 = $152,261.
- Future balance: $19,348 + $152,261 = $171,609.
You put in $77,000 ($5,000 plus $72,000 of deposits), so $94,609 of the final balance, 55%, is growth.
Worked example 2: starting early or saving more?
Two savers earn 7%. Saver A starts at age 25 and puts in $300 a month for 40 years. Saver B waits until 35, then puts in $500 a month for 30 years.
| Saver A (age 25) | Saver B (age 35) | |
|---|---|---|
| Monthly deposit | $300 | $500 |
| Years saving | 40 | 30 |
| Total contributed | $144,000 | $180,000 |
| Balance at 65 | $741,463 | $584,726 |
Saver A puts in $36,000 less but finishes with $156,736 more, because the extra ten years compound. This is an illustration, since real returns vary from year to year.
Worked example 3: raising your deposit each year
Take example 1 and increase the monthly deposit by 3% a year, roughly what a raise might allow.
| Flat $300 a month | Rising 3% a year | |
|---|---|---|
| Total contributed | $77,000 | $101,733 |
| Balance after 20 years | $171,609 | $210,956 |
A modest yearly increase adds $39,346 to the final balance, because bigger deposits are made while the earlier ones are already growing.
Worked example 4: what a 1% yearly fee costs
Someone saves $300 a month for 30 years. In one case the investment earns 7% with no fees. In the other it earns 7% but charges a 1% yearly fee, leaving 6%.
| 7% (no fee) | 6% (after a 1% fee) | |
|---|---|---|
| Total contributed | $108,000 | $108,000 |
| Balance after 30 years | $350,836 | $292,354 |
A 1% fee looks small, but here it costs $58,482, or 17% of the final balance. Fees compound against you just as returns compound for you.
A lump sum left alone
$10,000 invested once with no further deposits:
| Annual return | After 10 years | After 20 years | After 30 years |
|---|---|---|---|
| 4% | $14,802 | $21,911 | $32,434 |
| 7% | $19,672 | $38,697 | $76,123 |
| 10% | $25,937 | $67,275 | $174,494 |
The Rule of 72 against the exact answer
| Annual return | Rule of 72 estimate | Exact years to double |
|---|---|---|
| 4% | 18.0 years | 17.7 years |
| 6% | 12.0 years | 11.9 years |
| 8% | 9.0 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
The shortcut is close enough for quick planning.
Three levers you control
- Time. Starting ten years earlier can matter more than saving much more later.
- Deposit size. Raising your deposit each year, even by a few percent, boosts the final balance noticeably.
- Fees and taxes. A small yearly fee compounds against you just as returns compound for you.
Common mistakes to avoid
- Assuming a high return is guaranteed. Use a conservative rate and try lower ones too.
- Ignoring inflation. A large future balance buys less than the same number does today.
- Ignoring fees and taxes. Both reduce the growth you actually keep.
- Waiting for a perfect moment to start. Time invested matters more than timing.
- Raiding the account. Withdrawals interrupt compounding.
This tool illustrates arithmetic, not a forecast. Investment returns vary from year to year and can be negative. For retirement plans see the 401(k) calculator.
Sources and review
The calculation is the standard future-value formula, tested against closed-form results. To check our results against an independent tool, the US Securities and Exchange Commission's Investor.gov compound interest calculator uses the same idea. Last reviewed September 2026. Read about our methodology.