## Present Value of a Future Amount

The present value of a future amount is the current worth of a future sum of money or stream of cash flows, given a specified rate of return (or discount rate). It’s a financial concept that’s based on the principle that money available today is worth more than the same amount in the future due to its potential earning capacity, also known as the time value of money.

Present value is calculated using the following formula:

PV = FV / (1 + r)^n

Where:

- PV is the present value
- FV is the future value (the amount of money to be received in the future)
- r is the discount rate (the rate of return required by an investor)
- n is the number of periods (such as years) until the future payment will be received

This formula discounts the future value to today’s dollars, allowing you to compare amounts of money from different time periods on equal terms. For example, if you wanted to determine the value in today’s dollars of $1,000 to be received in 5 years, assuming an annual discount rate of 6%, you would use the present value formula to calculate this amount.

## Example of the Present Value of a Future Amount

Suppose you are promised to receive $1,000 five years from now. You want to know the present value of this future payment, assuming an annual discount rate of 5%.

Here’s how you can calculate it using the formula:

PV = FV / (1 + r)^n

Substitute the given values into the formula:

PV = $1,000 / (1 + 0.05)^5

Perform the calculation:

PV = $1,000 / 1.27628

So:

PV = $783.53

Therefore, the present value of $1,000 received 5 years from now, discounted at an annual rate of 5%, is approximately $783.53. This means that, assuming a 5% return per year, you’d be indifferent between receiving $783.53 today and $1,000 five years from now.