Guide
The future value formula, explained
Every variable, both formulas, the spreadsheet equivalents and examples you can verify in the future value calculator.
The two formulas
Lump sum: FV = PV × (1 + r/n)n×t
Regular payments: FV = PMT × (((1 + r/n)n×t − 1) ÷ (r/n))
When you have both a starting balance and ongoing contributions, add the two results together. That is exactly what the calculator does, which is why it reports the growth of the starting amount separately from the growth of contributions.
What each variable means
- PV — present value, the amount invested today.
- PMT — the equal payment made each period.
- r — the nominal annual rate, as a decimal (7% = 0.07).
- n — compounding periods per year: 1, 4, 12 or 365.
- t — the number of years.
Worked example, step by step
$10,000 at 7% compounded monthly for 20 years. The periodic rate is 0.07 ÷ 12 = 0.0058333, and the period count is 12 × 20 = 240. (1.0058333)240 ≈ 4.0387, so FV ≈ $40,387. Add $500 a month and the annuity term contributes roughly $260,500, for about $300,900 in total.
Nominal vs real (inflation-adjusted)
Divide the result by (1 + i)t, where i is your inflation assumption, to state the balance in today’s money. At 2% over 20 years the $300,900 above is worth about $202,500 in current spending power.
Spreadsheet equivalents
Excel and Google Sheets both use =FV(rate, nper, pmt, [pv], [type]). Keep the rate and period count in the same unit, enter payments as negatives, and set type to 1 for payments at the start of each period.
Where the formula stops being useful
It assumes one constant rate, no tax and no fees. Real returns arrive unevenly, and the order of good and bad years matters when you are withdrawing. Use future value to compare scenarios, not to forecast a single certain number.
Frequently asked questions
What is the future value formula?
FV = PV x (1 + r/n)^(n x t) for a lump sum, where PV is the present value, r the annual rate, n the compounding periods per year and t the years. Add PMT x (((1 + r/n)^(n x t) - 1) / (r/n)) when you also contribute each period.
What does n mean in the future value formula?
n is how many times interest compounds per year: 1 for annual, 4 for quarterly, 12 for monthly and 365 for daily. It divides the annual rate and multiplies the number of years, so both the periodic rate and the period count change with it.
Why does my answer differ from an online calculator?
Almost always because of compounding frequency, or because payments are assumed at the start rather than the end of each period. Check n first, then whether the tool models an ordinary annuity or an annuity due.