The Future Value of Money Formula
The future value of money formula is FV = PV × (1 + r)n. It tells you what a sum of money today will be worth in the future once it earns a rate of return: take the present amount (PV) and multiply it by the growth factor (1 + r) once for every period (n). At 7 percent compounded monthly, $10,000 becomes about $40,387 in 20 years. This guide explains the formula in plain terms, works through money examples, and shows how monthly compounding changes the result.
What is the future value of money formula?
The future value of money formula is the equation behind the time value of money — the idea that a dollar today is worth more than a dollar in the future, because today's dollar can be invested and grow. For a single sum, the formula is:
It takes an amount of money you have now, applies a rate of return for each period, and returns what that money will be worth after a number of periods. That is all future value is: a present amount pushed forward in time by compounding. This page focuses on applying it to real money; for the deeper algebra — including rearranging it to solve for the rate or the time — see the full future value formula guide.
The formula and what each part means
Every term maps to something concrete:
- FV — the future value, the amount of money you end up with.
- PV — the present value, the sum of money you have today.
- r — the rate of return for one period, written as a decimal, so 7 percent is 0.07.
- n — the number of periods the money compounds for.
The one rule that matters most: r and n must use the same time unit. If interest compounds monthly, r is the monthly rate (the annual rate divided by 12) and n is the number of months. Written out for monthly compounding, the formula becomes FV = PV × (1 + annual rate / 12)years × 12, which is exactly what this site's calculators use.
How the formula works, step by step
Take $10,000 at a 7 percent annual return, compounded monthly. First convert the inputs to monthly terms: the monthly rate is 0.07 ÷ 12, and 20 years is 240 months. Then apply the growth factor once per month:
- After one month, the balance is $10,000 × (1 + 0.07/12) = about $10,058.
- Each following month multiplies the new balance by the same factor, so growth builds on growth.
- After 240 months, the balance is $10,000 × (1 + 0.07/12)240 = about $40,387.
The exponent is what makes this compound rather than simple growth. Applying (1 + r) once adds one period of return; applying it n times means every period's growth also earns returns in every later period. That is why the money more than quadruples even though the rate is only 7 percent.
Example: what $10,000 becomes
Here is $10,000 run through the formula at 7 percent, compounded monthly, over several horizons. The interest column is simply the future value minus the original $10,000.
| Years (n in months) | Future value | Interest earned |
|---|---|---|
| 5 years | $14,176 | $4,176 |
| 10 years | $20,097 | $10,097 |
| 20 years | $40,387 | $30,387 |
| 30 years | $81,165 | $71,165 |
Skip the hand calculation: the future value of money calculator applies this exact formula instantly — enter an amount, a rate and a time period and watch the balance build.
Monthly vs annual compounding
The same headline rate produces different results depending on how often it compounds, because more frequent compounding applies the growth factor more times. Watch what happens to $10,000 at 7 percent over 20 years when only the compounding frequency changes:
| Compounding | r and n used | Future value |
|---|---|---|
| Annually | r = 0.07, n = 20 | $38,697 |
| Monthly | r = 0.07/12, n = 240 | $40,387 |
Monthly compounding earns about $1,690 more on the same money at the same rate — purely because interest starts earning interest twelve times a year instead of once. This site uses monthly compounding throughout, so its figures line up with the monthly row.
Using the formula for real money decisions
The formula is the engine behind most everyday money questions, but the single-sum version only covers a one-time amount. Match the situation to the right tool:
- A lump sum growing on its own — use FV = PV(1 + r)n directly, or the future value of money calculator.
- Regular contributions — add the annuity formula; the future value of annuity calculator does this for you.
- Seeing the result in today's money — strip out inflation with the future value of money inflation calculator.
Whatever the case, the honest way to use the formula is to write the rate as a decimal, match your periods, lean toward a conservative rate, and remember the answer is a nominal projection, not a guarantee.
Assumptions behind the formula
- A constant rate. The formula applies the same rate every period; real returns move around year to year.
- Matched periods. r and n share a time unit — monthly rate with months, annual rate with years.
- A single sum. FV = PV(1 + r)n values one amount; recurring deposits need the annuity formula added on.
- Nominal dollars. The result is before inflation and tax, both of which reduce real growth.
Frequently asked questions
The bottom line
The future value of money formula, FV = PV(1 + r)n, is the compact way of saying “money invested today grows by its rate of return, compounding every period.” Read the four variables, keep r and n on the same clock, and you can project what any lump sum becomes over time. Add the annuity formula when you contribute regularly, and adjust for inflation when you want the answer in today's purchasing power.
When you would rather not do it by hand, the future value of money calculator runs the formula instantly, and the full future value formula guide covers the algebra behind it.
Disclaimer: This guide is for general educational purposes only and is not financial advice. The examples use assumed rates of return to illustrate the formula; they are projections, not guarantees, and actual results vary with markets, inflation, taxes and fees. Consider speaking with a qualified financial professional before making decisions about your own money.