## Future Value

Future Value (FV) is a concept in finance that refers to the value of an asset or cash at a specific date in the future that is equivalent in value to a specified sum today. Future Value is used to evaluate the potential for investment or the profitability of a project.

The Future Value of a present amount of money can be calculated using the formula:

\(FV = PV \times (1 + r/n)^{nt} \)

Where:

- FV = Future Value
- PV = Present Value (the current amount of money)
- r = annual interest rate (in decimal form, so 5% would be entered as 0.05)
- n = number of times that interest is compounded per year
- t = time the money is invested for in years

This formula assumes that interest is compounded, meaning that interest is added to the principal amount and then itself earns interest.

## Example of Future Value

Suppose you deposit $5,000 into a savings account that offers an annual interest rate of 3%, compounded annually. You plan to keep this money in the savings account for 10 years.

The Future Value formula:

\(FV = PV \times (1 + r/n)^{nt} \)

where:

- FV = Future Value
- PV = Present Value (the current amount of money)
- r = annual interest rate (in decimal form, so 3% would be entered as 0.03)
- n = number of times that interest is compounded per year
- t = time the money is invested for in years

For this example, the values are:

- PV = $5,000
- r = 0.03
- n = 1 (since the interest is compounded annually)
- t = 10

So, you substitute these values into the formula to get:

\(FV = \$5,000 \times (1 + 0.03/1)^{1*10} \)

\(= \$5,000 \times 1.03^{10} \)

\(= \$5,000 \times 1.34392 \)

= $6,719.60

So, your $5,000 would grow to approximately $6,719.60 after 10 years in this savings account.