Future Value Calculator

What is Future Value?

Future Value (FV) is a financial concept that estimates the value of an asset or cash at a specified date in the future, based on an assumed growth rate. It's a fundamental principle in finance used for investment planning, retirement savings, and evaluating the long-term potential of various financial decisions.

The Future Value Formula

The formula for calculating Future Value is:

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

Where:

• \(FV\) = Future Value
• \(PV\) = Present Value (initial investment)
• \(r\) = Annual interest rate (in decimal form)
• \(n\) = Number of times interest is compounded per year
• \(t\) = Number of years

Step-by-Step Future Value Calculation

1. Identify the present value (PV), annual interest rate (r), compounding frequency (n), and time period (t).
2. Convert the annual interest rate to decimal form (divide by 100).
3. Divide the annual rate by the compounding frequency to get the periodic rate.
4. Multiply the compounding frequency by the number of years to get the total number of compounding periods.
5. Plug these values into the Future Value formula.
6. Calculate the future value (FV).
7. Subtract the present value from the future value to get the growth.

Example Calculation

Let's calculate the Future Value for an initial investment of $10,000, with an annual interest rate of 5%, compounded monthly, over 10 years:

1. \(PV = \$10,000\), \(r = 5\% = 0.05\), \(n = 12\) (monthly compounding), \(t = 10\) years
2. Periodic rate = \(0.05 \div 12 = 0.004167\)
3. Total compounding periods = \(12 \times 10 = 120\)
4. \(FV = 10000(1 + 0.004167)^{120} = \$16,470.09\)
5. Growth = \$16,470.09 - \$10,000 = \$6,470.09

Visual Representation

The green portion represents the initial investment ($10,000), and the blue portion represents the growth ($6,470.09).