How the future value is computed
This calculator handles the case where you invest a lump sum and keep adding money every month. Because the compounding option (annual, semi-annual, quarterly, monthly or daily) may not match the monthly contributions, it works in two steps:
- Convert the stated annual rate
iand compounding frequencyninto an effective annual rate:EAR = (1 + i/n)^n − 1. - Convert that into an equivalent monthly rate:
m = (1 + EAR)^(1/12) − 1.
It then runs month by month: balance = balance × (1 + m) + contribution. The inflation option divides the result by (1 + inflation)^years. Contributions are added at the end of each month.
Worked example
Invest 10,000 up front plus 300 a month at 8%, compounded monthly, for 20 years (240 months). Monthly compounding gives m = 0.08/12 = 0.6667%, and (1.006667)^240 is about 4.927.
- Initial amount grows to 10,000 × 4.927 = 49,268
- Monthly contributions grow to 300 × (4.927 − 1) ÷ 0.006667 = 176,706
- Future value: about 225,974
- Contributed: 10,000 + 300 × 240 = 82,000; growth is about 143,974
Effect of the compounding setting
Same example, only the compounding frequency changed:
| Compounding | Future value |
|---|---|
| Annually | about 217,309 |
| Quarterly | about 224,307 |
| Monthly | about 225,974 |
| Daily | about 226,796 |
The spread is under 5% across all options. The return, the time horizon and how much you contribute matter far more than the compounding label. Most index funds and brokerage accounts effectively grow continuously, so monthly or daily is the closer match.
When it fits and when it doesn't
- Good for: comparing savings plans, such as 200 a month versus 400, or testing how much starting 5 years earlier changes the outcome.
- Return assumptions: enter a return net of fund fees. A 1% annual fee on an 8% gross return is a 7% net return, which in the example above lowers the result from about 226,000 to about 196,700.
- Nominal versus real: a 226,000 balance in 20 years is not 226,000 of today's purchasing power. Tick the inflation box to see the real value; at 3% that is about 125,000.
- Not modeled: taxes on gains, contributions that rise with your salary, withdrawals, and year-to-year volatility.
For a lump sum with no contributions use the compound interest calculator. For a long-horizon goal see the retirement calculator, and for judging returns see the ROI calculator. The compound interest guide explains the formula in depth.