# Present Value Calculator

Calculate the present value of an investment given its future value, the rate, and time using the PV calculator below.

$% years ## Results:  Present Value:$729.88 Total Interest: $270.12 This calculation is based on widely-accepted formulas for educational purposes only - this is not a recommendation for how to handle your finances, and it is not an offer to lend or invest. Consult with a financial professional before making financial decisions. Learn how we calculated this below ## On this page: ## How to Calculate Present Value If you receive payments over time, the present value is what those payments are worth today. You can think of present value as the current value of those payments without compound interest accrued. You can also calculate the present value of an investment. If you are investing for a future goal, the present value tells you what you need to invest today to achieve that goal. To calculate present value, enter the future value, interest rate, and time period into the present value calculator above. You can also do this without a calculator using a simple formula. ### Present Value Formula The present value formula is: PV = \frac{FV}{(1 + r)^{n}} Where: PV = present value FV = future value r = interest rate n = number of periods For example, let’s assume you want to retire in 40 years with$2 million. You believe that you can earn an average rate of return of 10% over this timeframe. How much will you need to invest today to meet your retirement goals?

PV = \frac{\$2,000,000}{(1 + 0.1)^{40}} PV = \frac{\$2,000,000}{1.1^{40}}
PV = \frac{\$2,000,000}{45.25926} PV = \$44,189.86

You would need to invest a little more than $44,000 to end up with$2 million at the end of 40 years, assuming an average rate of return of 10%. As the present value calculator shows, almost all the growth is due to interest received.

## How to Find the Present Value of an Annuity

The present value of an annuity can be calculated using our annuity calculator (under the present value tab). But, you can also apply the present value of annuity formula to calculate it yourself.

### Present Value of an Annuity Formula

The formula to calculate the present value of an annuity is:

PV = PMT \times \left [ \frac{1 − (1 + i)^{−n}}{i} \right ]

Where:
PV = present value of an ordinary annuity
PMT = payment amount
i = interest rate
n = number of payments

For example, let’s assume you will receive an annuity payment of $2,000 each year for 5 years at an annual interest rate of 6.5%. PV = \$2,000 \times \left [ \frac{1 − (1 + 0.065)^{−5}}{0.065} \right ]
PV = \$2,000 \times \left [ \frac{1 − 1.065^{−5}}{0.065} \right ] PV = \$2,000 \times \left [ \frac{1 − 0.7299}{0.065} \right ]
PV = \$2,000 \times \left [ \frac{0.2701}{0.065} \right ] PV = \$2,000 \times 4.156
PV = \$8,310.77 So, the present value of this annuity is equal to$8,310.77.

You can also use our present value of an annuity calculator, which accounts for annual payments.

## Future Value vs. Present Value

The present value is what a future stream of payments is worth today, whereas the future value is what those streams of payments are worth at some point in the future.

In the earlier example, we looked at what amount should be invested today to end up with a certain amount at retirement.

The future value will be greater than the present value, assuming there is a positive interest rate. Since dollars today are worth more than dollars in the future, a higher dollar amount is needed in the future to equal a specific dollar amount today.

For example, $1,000 today is worth the same as$2,593.74 10 years from now, assuming a 10% interest rate for your investment. In this example, $1,000 is the present value, and$2,593.74 is the future value.

You can also use our interest calculator to calculate the future value.

## Net Present Value

Net present value (NPV) is a tool used in corporate finance and capital budgeting to value a potential investment opportunity. It is similar to the present value formula shown above but subtracts the initial investment at the end.

The interest rate used here is what the corporation can earn on other similar investments.

Let’s look at an example to see how it is used.

A corporation has an investment opportunity in which it will pay $1,000,000 upfront for a new machine, and after 5 years, the new machine will save the company$4,000,000. If the company has an internal rate of return of 15%, should it proceed with the investment?

We can write the NPV as shown below and refer to the initial cash outflow as ICO.

NPV = \frac{FV}{\left ( 1 + r \right )^{n}} − ICO
NPV = \frac{\$4,000,000}{\left ( 1 + 0.15 \right )^{5}} − \$1,000,000
NPV = \frac{\$4,000,000}{1.15^{5}} − \$1,000,000
NPV = \frac{\$4,000,000}{2.01136} − \$1,000,000
NPV = \$1,988,706.94 − \$1,000,000
NPV = \$988,706.94 Since the NPV is positive, the business should go forward with the investment. If the NPV was negative, the business would want to avoid it. For example, if the future value was only$1,500,000, the business would be better off not purchasing the new machine.

Contrary to the earlier retirement scenarios, a higher present value here is more advantageous than a lower present value.

## Why is Present Value Important?

Present value (and the time value of money as a whole) plays an important role in many financial decisions.

As we have shown in our examples, individuals use it to forecast how much they will need to invest today to meet retirement goals, businesses use it when deciding to invest in capital, and investors use it to value stocks or bonds.

Present value allows you to compare the value of dollars today with the value of dollars at a specific time in the future. The time value of money plays an important role for all individuals—if you bank, borrow, or invest, you are impacted by the time value of money.