Compound interest calculator
Enter a principal, annual rate, term and compounding frequency (continuous included), add monthly or yearly contributions and get the future value, total invested, interest, growth multiple and a per-period schedule — plus reverse calculation of the rate or contribution.
Runs in your browserEvery computation happens in your browser — your data never leaves this device.
Inputs
Interest compounds once per period and contributions are credited at the start or end of each period; continuous compounding uses e^(r·t). Everything runs locally in your browser.
Results
181,939.67100,000.0081,939.671.8194 ×6.17%0.00Period schedule
Each period follows the chosen compounding frequency — 120 periods in total; only the first 20 are listed.
| Period | Opening | Contribution | Interest | Closing |
|---|---|---|---|---|
| 1 | 100,000.00 | 0.00 | 500.00 | 100,500.00 |
| 2 | 100,500.00 | 0.00 | 502.50 | 101,002.50 |
| 3 | 101,002.50 | 0.00 | 505.01 | 101,507.51 |
| 4 | 101,507.51 | 0.00 | 507.54 | 102,015.05 |
| 5 | 102,015.05 | 0.00 | 510.08 | 102,525.13 |
| 6 | 102,525.13 | 0.00 | 512.63 | 103,037.75 |
| 7 | 103,037.75 | 0.00 | 515.19 | 103,552.94 |
| 8 | 103,552.94 | 0.00 | 517.76 | 104,070.70 |
| 9 | 104,070.70 | 0.00 | 520.35 | 104,591.06 |
| 10 | 104,591.06 | 0.00 | 522.96 | 105,114.01 |
| 11 | 105,114.01 | 0.00 | 525.57 | 105,639.58 |
| 12 | 105,639.58 | 0.00 | 528.20 | 106,167.78 |
| 13 | 106,167.78 | 0.00 | 530.84 | 106,698.62 |
| 14 | 106,698.62 | 0.00 | 533.49 | 107,232.11 |
| 15 | 107,232.11 | 0.00 | 536.16 | 107,768.27 |
| 16 | 107,768.27 | 0.00 | 538.84 | 108,307.12 |
| 17 | 108,307.12 | 0.00 | 541.54 | 108,848.65 |
| 18 | 108,848.65 | 0.00 | 544.24 | 109,392.89 |
| 19 | 109,392.89 | 0.00 | 546.96 | 109,939.86 |
| 20 | 109,939.86 | 0.00 | 549.70 | 110,489.56 |
| Summary | 100,000.00 | 0.00 | 81,939.67 | 181,939.67 |
What this tool does
- Project a pension or long-term savings pot: enter the principal, annual rate and term to see what monthly compounding really produces, with optional monthly or yearly contributions.
- Compare compounding frequencies — the same 6% rate compounded monthly, daily or continuously gives different future values, and the gap is right there.
- Work backwards from a goal: say you want 1,000,000 in ten years and the tool tells you the monthly contribution required or the annual rate you need to hit.
- Understand the shape of the growth: total invested, total interest and the growth multiple come together, and the per-period schedule shows when interest overtakes the principal.
Example
Input
Principal 10,000, 6% annual rate, 10 years, monthly compounding, no contributions
Output
Future value 18,193.97; total invested 10,000.00; total interest 8,193.97; growth multiple 1.82; CAGR 6.17%; 120 periods at 0.5% each
The CAGR reads 6.17% rather than 6% because it is derived from the future value (future value ÷ principal, raised to 1/years, minus 1) — the extra 0.17% is exactly what monthly compounding adds.
Frequently asked questions
Why does the CAGR differ from the annual rate?
The annual rate is nominal; what you actually end up with depends on the compounding frequency and the contributions. CAGR is derived from future value and principal alone (future value ÷ principal to the power of 1/years, minus one) with contributions excluded. With a principal of zero it cannot be derived and is left blank.
How does continuous compounding work here?
Continuous compounding grows by e^(r·t): the number of periods is 12 when contributions are monthly and 1 when they are yearly, and each period is multiplied by the matching exponential. It is the limit of compounding frequency and gives the highest future value at the same rate, though the gap to daily compounding is already small.
How much does beginning-of-period versus end-of-period matter?
A beginning contribution is invested before the period’s interest is applied, so it earns interest for the whole period and lifts the future value. An end contribution is added after interest accrues, so the first one misses one period of interest. The difference is roughly one period’s worth of interest.
What happens with invalid input?
Principal and contributions cannot be negative, years must be greater than 0 and at most 200, the annual rate must be above -100% and at most 10000%, and a target value must be positive. Out-of-range input shows the matching message instead of a result; negative rates are allowed so you can model losses.
Why does the reverse calculation not land exactly on the target?
It uses bisection with 200 iterations, which drives the error down to 1e-9, but amounts are normally rounded to cents, so depositing the suggested figure leaves a tiny remainder. If the target is unreachable under the current inputs — a required rate above 500%, for instance — the tool says so instead of returning a number.
Keywords：compound interestfuture valuecagrsavingscontinuous compounding复利复利计算终值年化收益率定投