# Present Value Calculator (and the Present Value Formula)

Written by:
PK

On this page is a present value calculator, sometimes abbreviated as a PV Calculator. Present value is an estimate of the current sum needed to equal some future target amount to account for various risks. Using the present value formula (or a tool like ours), you can model the value of future money.

### Using the Present Value Calculator

• Future Amount – The amount you'll either receive or would like to have at the end of the period
• Interest Rate Per Year (Discount Rate) – The annual percentage rate investment return you'd earn over the period of your investment
• Number of Years – The total number of years until the future sum is received, or the total number of years until you need a future sum. (You can enter fractional years, such as 6.5)
• Present Value ($) – The amount the future sum is worth today with the assumptions in the input fields ## The Present Value Formula The general solution comes in this formula: PV=\frac{C}{(1+i)^n} where: • C = Future sum • i = Interest rate (where '1' is 100%) • n= number of periods ### Example Using the Present Value Formula In the simplest case, let's say you're an excellent investor and can get a 10% return on your money. You have$100 today, and you stay invested for three years:

Start:    $100 Year 1:$110
2:  $121 3:$133.10

If I asked you for $100 today, promising to give you$120 at year three... I'd hope you'd turn that down. The present value of $120 in three years, if you have alternatives that earn 10%, is actually$90.16.

That is to say, the present value of $120 if your time-frame is 3 years and your discount rate is 10% is$90.16.

For the above problem, your sum would be $133.10. Here's how the math works out: Inputs:$133.10 in 3 years given 10% investment returns

PV = 133.10 / (1+.1)^3

= 133.10 / 1.1^3

= 133.10 / 1.331

PV = $100.00 and for my generous offer of$120:

Inputs: $120.00 in 3 years given you could get 10% investment returns elsewhere PV = 120 / (1+.1)^3 =$90.16

I hope you'd agree now. If you can make 10% a year you should turn down my offer of $120 in three years for$100 today.

## Why is present value important?

Future quantities deal with both inflationary (or deflationary) pressures, opportunity costs, and other risks to the value of your final sum. The actual equivalent value of a sum in the future is (almost) never the same amount as having a lump sum today.

That's where 'Present Value' comes into play.

If you have a return estimate for what you could earn with a lump sum investment today, you can easily estimate what that future value is worth. Alternatively, present value also tells you the amount you would need to invest today if you needed to end up with the final lump sum assuming a given return... just know that forecasting of this sort is never better than an educated guess!

## Using the Present Value Formula and Calculator to Value Investments and Tradeoffs

While we're insinuating that 10% is an unreasonable discount rate, there will always be tradeoffs when you're dealing with uncertainty and sums in the future.

For a real-life investment measure, take a look at our Dow Jones Return Calculator.

After dividends and inflation are factored in, you would have seen about a 10% return, ignoring taxes and fees, since the Dow Jones Industrial Average has existed. (Remember, only adjust for inflation if you also adjust the final amount for inflation as well!) We're not sure if that's an accurate return estimate going forward, so please form your own estimate.

Regardless of your number, when you forego money today, you're giving something up in the future. That's true even if you're only able to make 1% on your money reliably.

And, yes, sometimes it's possible that a return of capital may be more important than a return on capital. In that sort of scenario money in the future would be worth more than today.

## When should you use present value estimates?

Other than while evaluating investments, present value estimates are useful for evaluating job offers.

Many of you readers are in industries which have some sort of equity or variable compensation in your annual income. Any honest accounting of an offer evaluates your compensation other than salary, such as stock, options, or bonuses with some sort of a present value calculation (Total Compensation).

Bonuses are first to go in a recession, options can go to zero (especially in early stage companies) and stock can go up, down.. or even to zero.

Future values are actually a range of possible values... some of them zero.

Every dollar of current salary is more valuable than variable compensation... although it doesn't have the upside of variable pay, it is safer than other income forms. When using the present value calculator you can adjust for that uncertainty by reducing the amount of future value and running the numbers again.

We hope you enjoyed this brief look at evaluating investments using the present value formula. Keep this concept in mind whenever you evaluate your options going forward.

### What other calculators do you have?

Try our other financial basics and valuation calculators:

### PK

PK started DQYDJ in 2009 to research and discuss finance and investing and help answer financial questions. He's expanded DQYDJ to build visualizations, calculators, and interactive tools.

PK lives in New Hampshire with his wife, kids, and dog.

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