Future Value Calculator

FV = PV × (1 + r ÷ m)^(m × t)

PV

The present value — the sum you are setting aside today

r

The annual rate of return, written as a decimal

m

How many times a year the growth is credited

t

The number of whole years the money stays invested

FV

The future value — what the sum becomes at the end of the term

Reach for it when you have a target date in mind and want to know what a sum becomes by then, rather than when you have a target balance and want to know what to put in. Setting the rate to zero is the right way to answer a different and surprisingly common question — what will this be worth if it simply sits there — and the answer comes back as the same number you typed, with a multiple of exactly one. The most useful thing the page does is let you hold the term fixed and walk the rate, which is what the table below does: six rates across one decade of growth for the same 10,000. Run your own two candidate rates through the calculator rather than reading across from a row, because the table is a fixed 10,000 at a fixed ten years.

1. 10,000 at 7% for ten years, compounded annually

   1. Annual compounding means one period a year, so the periodic rate is 7 ÷ 100 = 0.07
   2. Periods: 10
   3. Balance: 10,000 × 1.07^10 = 19,671.51
   4. Growth: 19,671.51 − 10,000 = 9,671.51
   5. Multiple: 19,671.51 ÷ 10,000 = 1.9672

   This is the page's default. The multiple is the useful half of the answer: it says the money nearly doubles, and it says so without needing to know whether you started with ten thousand or a quarter of a million.

2. 50,000 at 6% for twenty-five years, compounded annually

   1. Periodic rate: 6 ÷ 100 = 0.06 a year
   2. Periods: 25
   3. Balance: 50,000 × 1.06^25 = 214,593.54
   4. Growth: 214,593.54 − 50,000 = 164,593.54
   5. Multiple: 214,593.54 ÷ 50,000 = 4.2919

   Compare this with the default above: five times the money and two and a half times the term, but a balance nearly eleven times as large. The first twenty-five years of a long compounding run do most of the work in the last few.

3. 10,000 at 7% for ten years, compounded monthly

   1. Periodic rate: 7 ÷ 100 ÷ 12 = 0.00583333 a month
   2. Periods: 12 × 10 = 120
   3. Balance: 10,000 × 1.00583333^120 = 20,096.61
   4. Growth: 20,096.61 − 10,000 = 10,096.61
   5. Multiple: 20,096.61 ÷ 10,000 = 2.0097

   The same money, the same rate and the same ten years as the default, differing only in how often the growth is credited — and the difference is 425.10. Because the compounding frequency here is a field rather than an assumption, you can see exactly what it costs to accept a quoted rate without asking how often it is applied.

The page projects one sum forward and assumes three things that usually will not hold. First, that the rate is constant: a real portfolio does not return 7% every year, it returns 22% one year and loses 9% the next, and two portfolios with the same average return can end up in different places depending on the order the years arrive in. Second, that nothing is added or taken out — one deposit at the start and no touching it, so a plan with monthly contributions cannot be answered here. Third, that the time is a whole number of years, because half a compounding period has no single meaning once the frequency is anything other than annual. Tax is not modelled, and for a taxable account the drag is real: if the growth were taxed at 30% every year, the 7% default would behave like 4.9% and the balance would be 16,134.48 rather than 19,671.51. Inflation is absent, so every figure is nominal — 19,671.51 in ten years is not 19,671.51 in today's purchasing power. No currency symbol is attached, so the numbers are right in whatever currency you typed and wrong in any other.

What does future value mean?

It is what a sum of money today becomes at some point in the future once it has been left to grow at a given rate. Put 10,000 into a calculator with a 7% annual rate and a ten year term with annual compounding and the future value is 19,671.51. It is the mirror image of present value, which asks the opposite question: what is a sum arriving in ten years worth today.

How do I calculate future value by hand?

Multiply the amount by one plus the periodic rate, raised to the number of periods. The periodic rate is the annual rate divided by how many times a year the growth is credited; the number of periods is that same number multiplied by the years. For 10,000 at 7% over ten years with annual compounding that is 10,000 × 1.07^10, which is 19,671.51. Growth of 9,671.51 is the difference between that and the 10,000 you started with.

What is a good annual rate to assume?

There is no honest single answer, and the number you pick will drive the whole result — which is exactly why the table on this page walks six rates across the same ten years. Long-run equity returns have historically run in the high single digits before inflation and fees, government bonds well below that, and cash below that again. Using a rate you cannot justify is the fastest way to get a future value that means nothing, so pick a rate you can name a source for and check the answer at two rates rather than one.

Does the compounding frequency matter here?

It matters, and it is the one input people leave at whatever the page defaulted to. At 7% over ten years, 10,000 becomes 19,671.51 with annual compounding and 20,096.61 with monthly compounding — a difference of 425.10 for the same rate and the same term. Compounding more often always helps a saver and always costs a borrower, and the effect grows with both the rate and the length of the term.

Why does a longer term change the answer so much more than the rate?

Because the years sit in the exponent while the rate sits only in the base, so the term multiplies the whole curve rather than shifting it. At 6%, 10,000 becomes 17,908.48 in ten years and 42,918.71 in twenty-five — the term alone is worth 2.4 times the balance. Raising the rate from 6% to 7% over those same twenty-five years takes it from 42,918.71 to 54,274.33, which is 1.26 times. That is the time value of money stated plainly: the years are what let compound growth do its work, and no rate makes up for not having them.

Is the future value the same as the money I will actually have?

Not quite. The figure is nominal — it is the number of currency units you would see, before tax and before inflation, and it assumes the rate held for every one of the years. Tax on the growth is taken as it arises in a taxable account, and inflation reduces what the balance buys. The future value is the right starting point for all of those questions, but it is a projection made from the inputs you gave rather than a statement about what will happen.

• Compound Interest Calculator — a second implementation of the same closed form — U.S. Securities and Exchange Commission (Investor.gov)
• H.15 Selected Interest Rates — the published rate series a projected annual return stands in for — Board of Governors of the Federal Reserve System (United States)
• 12 CFR Part 1026, Appendix J — the periods-per-year convention used when the frequency is not annual — Electronic Code of Federal Regulations (United States)