Future Value Factor Calculator

What this calculator does

This calculator does not tell you how much money you will have. It gives you the multiplier, the number you multiply money by. Feed it a rate and a number of periods, and it returns the future value factor, formally the future value interest factor:

Future value factor = (1 + rate)^periods

Notice what is missing from that formula: any amount of money. The factor describes what a given stretch of time at a given rate does to a sum, without caring what the sum is. Multiply any present amount by it and you get that amount's future value. That absence is not a gap in the tool. It is the entire point of it.

Why a bare number is more useful than an answer

An answer settles one question. A factor settles every question with the same rate and term, which is why this tool is worth having next to a plain future value calculator rather than instead of it.

Suppose you are looking at ten years at 5 percent. The factor is 1.6289. Now you can price anything against those conditions without recalculating: a 250,000 deposit becomes 407,223.66, a 40,000 one becomes 65,155.79, and a stray 1,800 becomes 2,932.01. One number, applied over and over. If you are comparing several amounts, or checking a set of figures, working with the factor is faster than running each case from scratch and easier to sanity-check, because you are only ever multiplying.

It reads well as a percentage too. A factor of 1.6289 means the money ends up at about 163 percent of what it started as, so the total growth over the ten years is 62.89 percent. That is a more honest way to describe a decade at 5 percent than the annual rate alone, which tends to sound smaller than it turns out to be.

Before calculators were on every desk, these factors were printed in long tables at the back of finance textbooks, and you looked yours up at the intersection of a rate column and a period row. Software has largely retired the tables, and OpenStax's text says as much. The factor itself never went anywhere, because it is what the software is computing.

How to use it

1. Interest rate per period. The rate earned in a single period, as a percent.
2. Number of periods. How many of those periods pass.

Press Calculate for the factor, which is shown to four decimal places, or Reset to clear the fields. Then multiply any present amount by it. As with every periodic calculation, the rate and the period count must describe the same unit of time, so monthly periods need the monthly rate.

A worked example you can check

Take 5 percent a period for 10 periods.

• Factor: 1.05¹⁰ = 1.6289
• Total growth over the ten periods: 62.89 percent
• Applied to 250,000: 250,000 × 1.6289 = 407,223.66
• Applied to 40,000: 40,000 × 1.6289 = 65,155.79

That single figure of 1.6289 is now doing all the work, whatever amount you point it at. And it has a second job, which is the more interesting half of what a factor is for.

Turn it upside down and it discounts instead

Divide one by the future value factor and you get the present value factor, sometimes called the discount factor. As OpenStax puts it, the present value factor is simply the reciprocal of the future value factor, which makes sense because the two are doing exactly opposite things.

One divided by 1.6289 is 0.6139. So under the same conditions, ten years at 5 percent, any amount promised to you in the future is worth about 61.4 percent of that as cash today. A promise of 100,000 in ten years is worth 61,391.33 now. And the round trip closes perfectly: put 61,391.33 in at 5 percent for ten periods, multiply by 1.6289, and you are back to exactly 100,000.

That is genuinely useful, because it means one calculation answers questions in both directions. Multiplying pushes a sum forward in time. Dividing pulls a sum backward. Compounding and discounting are not two topics to learn separately, they are the same factor read left to right or right to left, and once you have the number in front of you, you own both directions of the trade between money now and money later.

The same factor is hiding inside the other formulas

Here is the reason this small number deserves a tool of its own. Once you recognise (1 + rate)^periods, you start seeing it everywhere in finance, because almost every time value formula is built out of it.

The future value of a single sum is just the amount times this factor. The annuity factor, which values a stream of equal payments, is this factor minus one, divided by the rate. Loan payment formulas, bond prices, and discounted cash flow valuations all contain it, sometimes several times over. The elaborate-looking expressions in those formulas are mostly arrangements of this one idea: what a period of growth does, applied a certain number of times.

So if the wider family of time value calculations has ever felt like a pile of unrelated formulas to memorise, this factor is the piece that connects them. Understand what it does, and the rest stop being separate rules and start being variations on a single one.

Questions people ask

What do I do with the factor once I have it?

Multiply any present amount by it to get that amount's future value under the same rate and term. The same factor works for any sum.

How is this different from a future value calculator?

A future value calculator asks for an amount and gives you one answer. This gives you the multiplier itself, which you can apply to as many amounts as you like without recalculating.

How do I get the discount factor?

Divide one by the future value factor. That gives you what a future sum is worth today under the same conditions, since the two factors are reciprocals.

Can I use this for regular payments?

Not directly. This factor is for a single sum. A stream of equal payments uses the annuity factor, which is built from this one but is not the same number.

References

The quantity one plus the rate raised to the number of periods is what OpenStax's finance text calls the future value interest factor, noting that it rises both as the number of periods grows and as the rate rises. The same text explains that the present value factor is the reciprocal of the future value factor, since the two perform opposite operations, and observes that printed factor tables have largely given way to calculators and spreadsheets.

1. OpenStax, Principles of Finance, 7.2 Time Value of Money (TVM) Basics. https://openstax.org/books/principles-finance/pages/7-2-time-value-of-money-tvm-basics
2. OpenStax, Principles of Finance, 7.4 Applications of TVM in Finance. https://openstax.org/books/principles-finance/pages/7-4-applications-of-tvm-in-finance