How to Calculate Future Value
Future value is what money grows to at a steady rate over time: a starting amount, plus any regular contributions, plus what they earn. The same arithmetic, run backward, answers four more questions: how much to start with, how much to add, what rate it takes, and how long it takes. Our free calculator solves for any one of the five. It is arithmetic at a rate you choose, not a forecast.
Open the future value calculator
The five numbers
- Starting amount (often called present value, or PV): what is there today.
- Contribution (often called the payment, or PMT): an amount added, or taken out, every month, quarter, or year.
- Rate of return: the yearly rate the balance compounds at, or for a loan, its interest rate (APR).
- Time: the number of years (or periods).
- Future value (FV): the balance at the end.
Know any four and the fifth follows. That is the whole idea behind a time value of money calculator.
The future value formula
For a starting amount alone, future value is the starting amount times (1 + i) to the power n, where i is the rate for one period and n is the number of periods. Every period, the balance earns i on everything already there.
Regular contributions add a second piece: the contribution times ((1 + i) to the power n, minus 1), divided by i. That sum counts each contribution and the growth it earns from the period after it goes in. When contributions go in at the start of each period instead of the end, each one earns one more period, so that piece is multiplied by (1 + i).
Put together, with contributions at the end of each period:
FV = PV × (1 + i)n + PMT × ((1 + i)n − 1) ÷ i
Solving for the starting amount or the contribution rearranges that one line. Time has its own closed form using logarithms. The rate does not: there is no formula for it, so a calculator finds it by trying rates until the balance lands on the target. At a rate of zero, the formula reduces to plain addition: the starting amount plus every contribution.
How to use ours
- Pick what you want to find: the future value, the starting amount, the contribution, the rate of return, or the time.
- Enter the other four. Every amount is a plain positive number. Mark the contribution as added or taken out, choose monthly, quarterly, or yearly, and choose whether it goes in at the start or the end of each period. Read the rate as a yearly growth rate (the default) or as a loan rate (APR). Three presets set the rate to the platform's own long-term planning assumptions for a savings account, a mostly-bonds mix, and a balanced mix. They are assumptions, not forecasts, and not a recommendation of any mix.
- Read the answer. It appears in its own box, with a sentence that states it in words, a chart, and a year-by-year table. Switch to solving for a different number and the answer you just found stays in its box. Nothing you enter is stored.
A worked example
The calculator opens on $10,000 today, $500 added at the end of each month, 5.7% a year (the balanced preset), for 20 years.
- Under these assumptions, $10,000 today plus $500 added every month grows to about $249,558 after 20 years at 5.7% a year.
- Of that, $130,000 is money put in: the $10,000 start plus $120,000 of contributions. The other $119,558 is growth.
| Year | Balance at start | Added | Growth | Balance at end |
|---|---|---|---|---|
| Year 1 | $10,000 | $6,000 | $725 | $16,725 |
| Year 5 | $39,289 | $6,000 | $2,395 | $47,684 |
| Year 10 | $86,328 | $6,000 | $5,076 | $97,404 |
| Year 15 | $148,391 | $6,000 | $8,613 | $163,005 |
| Year 20 | $230,277 | $6,000 | $13,281 | $249,558 |
Growth is small at first and large later: $725 in year 1, against $13,281 in year 20, on the same $6,000 a year of contributions. That is compounding: each year earns on all the growth before it.
Solving for each of the five
Starting from the same example, change one input and solve for a different number:
| Solve for | Change from the example | Answer |
|---|---|---|
| Future value | The opening example as it stands. | Under these assumptions, $10,000 today plus $500 added every month grows to about $249,558 after 20 years at 5.7% a year. |
| Starting amount | No contribution, and a future value of $250,000. | Under these assumptions, it takes about $82,497 today to reach $250,000 after 20 years at 5.7% a year. |
| Contribution | A future value of $500,000. | Under these assumptions, reaching $500,000 after 20 years at 5.7% a year from $10,000 today takes about $1,071 added every month. |
| Rate of return | A future value of $300,000. | Under these assumptions, $10,000 today plus $500 added every month ends at $300,000 after 20 years at a yearly rate of about 7.21%. |
| Time | A future value of $500,000. | Under these assumptions, $10,000 today plus $500 added every month first reaches $500,000 after 29 years and 7 months at 5.7% a year. |
The contribution can also be money coming out. Solve for the contribution with $1,000,000 today, nothing left at the end, and 30 years. Under these assumptions, $1,000,000 today could supply about $5,713 taken out every month for 30 years at 5.7% a year, with $0 left at the end. That is the same arithmetic as an annuity payment.
It works for a loan too. Read the rate as a loan rate (APR), mark a $625 payment as taken out at the end of each month, set the future value to $0, and solve for the starting amount over 30 years at 7.8%. Under these assumptions, it takes about $86,821 today to cover $625 taken out every month for 30 years at 7.8% APR, with $0 left at the end. That starting amount is the loan that payment pays off, the same figure a lender's calculator or a spreadsheet's PV function gives.
The calculator shows these same answers for these inputs, computed by the same code.
Why a spreadsheet can come out a little higher
A common way to run this example in a spreadsheet is =FV(5.7%/12, 240, -500, -10000). That treats 5.7% as a rate that compounds monthly, which works out to about 5.851% over a full year, and it returns about $254,167 instead of $249,558.
By default our calculator treats the rate as the yearly rate the balance actually compounds at. Each month earns about 0.463%, which comes to exactly 5.7% over twelve months. Neither is wrong; they read the same number differently. To get the spreadsheet's answer in the calculator, read the rate as a loan rate (APR): it then divides the rate evenly across the months, the way lenders and spreadsheets do, and gives $254,167 too. To match the default in a spreadsheet, use (1 + 5.7%) to the power 1/12, minus 1, as the monthly rate. The two readings agree exactly when contributions are yearly.
What it leaves out
- One steady rate. Real returns go up and down from year to year, and the order they arrive in matters, most of all once money is coming out. One steady rate cannot show that.
- Inflation. Every figure is in the dollars of the day it happens. A future balance buys less than the same number of dollars today; the Inflation Calculator shows how much less.
- Fees and taxes. Neither is modeled. Lower the rate to see their effect.
- Steady contributions. Real contributions rise, pause, and stop. This holds them at one amount, at one frequency, for the whole time.
The first item matters most. One steady rate makes every year look alike. Real returns do not arrive that way, and once money is coming out, a few poor years early can matter more than the average. What is sequence of returns risk? shows it with a worked example.
Related
- What a future balance buys in today's dollars: the Inflation Calculator.
- Drawing a balance down in retirement, with withdrawals that rise with inflation: the 4 percent rule calculator guide.
- Multi-Cycle Planning: all of the free tools.