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.
