How it works
The future value (FV) calculation is a foundational time-value-of-money operation: it projects what a dollar today becomes after a set number of years at a fixed periodic rate. This calculator implements the standard academic FV formula combining a single present-value lump sum with an optional series of level monthly contributions.
Unlike a compound-interest tool that emphasizes compounding frequency, or an investment calculator oriented toward portfolio planning, this tool isolates the FV equation itself. Monthly compounding is assumed so the contribution schedule aligns cleanly with the interest period. The output is a single nominal dollar figure representing the balance at the end of the term.
The formula
FV = PV × (1 + r/12)^(12n) + PMT × [((1 + r/12)^(12n) − 1) / (r/12)]
Where PV is the present value (starting lump sum), PMT is the fixed monthly contribution (treated as an ordinary annuity — deposits at the end of each period), r is the annual interest rate in decimal form, and n is the number of years. The expression splits into two parts: the first term grows the initial lump sum, and the second accumulates the monthly deposits with interest. When PMT is zero the second term vanishes, leaving the pure lump-sum case.
| Variable | Meaning | Units |
|---|---|---|
| PV | Present value (initial lump sum) | dollars |
| PMT | Monthly contribution | dollars per month |
| r | Annual interest rate | percent, entered as e.g. 7 |
| n | Time horizon | years |
Worked example
Take a present value of $10,000, a monthly contribution of $0, an annual rate of 7%, and a term of 15 years. With no ongoing deposits, only the lump-sum term applies.
- Convert the annual rate to a monthly periodic rate: r/12 = 0.07 / 12 = 0.00583333.
- Determine the total number of compounding periods: 12 × 15 = 180 months.
- Raise the growth factor to the 180th power: (1.00583333)^180 = 2.849657.
- Multiply by the present value: 10,000 × 2.849657 = $28,496.57.
So $10,000 today, compounded monthly at a 7% annual rate for 15 years, grows to approximately $28,496.57. This is the bare time-value-of-money result with no account type, no goal, and no narrative — just the formula in isolation.
Things to watch
The result is a nominal projection at a constant rate; real-world returns fluctuate, and taxes or fees will reduce the actual ending balance. Treat the figure as an estimate, not professional advice.
Two subtleties deserve attention. First, because contributions are modeled as an ordinary annuity (end-of-period deposits), the calculator slightly understates the result if you actually invest at the start of each month. Second, the monthly rate uses simple division (r/12) rather than the exact equivalent monthly rate that would compound to the stated annual yield. For a 7% nominal rate this difference is negligible, but at very high rates or long horizons the gap widens. If your account specifies an effective annual rate rather than a nominal one, convert it before entering.