Present Value (PV) Calculator

What is Present Value?

Present Value (PV) is a financial concept that determines the current worth of a future sum of money or stream of cash flows, given a specified rate of return. In other words, it answers the question: "What would be the value today of a payment or series of payments that I will receive in the future?"

The Present Value Formula

The formula for calculating Present Value is:

\[PV = \frac{FV}{(1 + r)^t}\]

Where:

• \(PV\) = Present Value
• \(FV\) = Future Value
• \(r\) = Interest rate (in decimal form)
• \(t\) = Number of time periods

Step-by-Step Present Value Calculation

1. Identify the Future Value (FV), interest rate (r), and time period (t).
2. Convert the interest rate to decimal form (divide by 100).
3. Add 1 to the decimal interest rate.
4. Raise this sum to the power of t (number of time periods).
5. Divide the Future Value by this result.

Example Calculation

Let's calculate the Present Value of $10,000 to be received in 5 years, assuming an interest rate of 5% per year:

1. \(FV = \$10,000\), \(r = 5\% = 0.05\), \(t = 5\) years
2. \(PV = \frac{10000}{(1 + 0.05)^5}\)
3. \(PV = \frac{10000}{1.27628}\)
4. \(PV = \$7,835.26\)

Visual Representation

The green portion represents the Present Value ($7,835.26), and the blue portion represents the difference between the Present Value and the Future Value ($2,164.74).