
Future Value
The Future Value of a cash flow represents the amount, at some time in the future, that an investment made today will grow to if it is invested to earn a specific interest rate. For example, if you were to deposit $100 today in a bank account to earn an interest rate of 10% compounded annually, this investment will grow to $110 in one year. This can be shown as follows:
At the end of two years, the initial investment will have grown to $121. Notice that the investment earned $11 in interest during the second year, whereas, it only earned $10 in interest during the first year. Thus, in the second year, interest was earned not only on the initial investment of $100 but also on the $10 in interest that was paid at the end of the first year. This occurs because the interest rate in the example is a compound interest rate.
The interest rate in the example is 10% compounded annually. This implies that interest is paid annually. Thus the balance in the account was $110 at the end of the first year. Thus, in the second year the account pays 10% on the initial principal of $100 and the $10 of interest earned in the first year. Thus, the $121 balance in the account after two years can be computed as follows:
If the money was left in the account for one more year, interest would be earned on $121, i.e., the initial principal of $100, the $10 in interest paid at the end of year 1, and the $11 in interest paid at the end of year 2. Thus the balance in the account at the end of year three is $133.10. This can be computed as follows:
A pattern should be becoming apparent. The Future Value of an initial investment at a given interest rate compounded annually at any point in the future can be found using the following equation: where
© 2002  2010 by Mark A. Lane, Ph.D.
