Final answer:
The correct definition of the future value of a $1,000 investment is that it is the value of the investment at any date after the initial investment date, generally accounting for interest or other earnings accrued.
Step-by-step explanation:
The correct definition of the future value of a $1,000 investment is option b: Future value is the value of the investment at any date after the initial investment date. The future value is the amount an investment is worth after one or more periods of time, often after accounting for interest or other earnings accrued during that time. Option a, which mentions discounting the investment, is actually describing the present value, not the future value. The present value is the current worth of a promised future amount of money or stream of cash flows, given a specified rate of return.
Future value is an important concept when considering the earnings potential of an investment over time. For example, using a simple interest rate, if you invest $1,000 at an annual interest rate of 8%, the future value of this investment after one year would be $1,080. However, if interest rates rise and similar investments are yielding 12%, the opportunity cost of your investment would be the additional earnings that could have been obtained by investing at the higher rate. Nonetheless, the future value of your original $1,000 remains dependent on the agreed-upon 8% interest rate.
An understanding of future value is crucial, especially when comparing investments, planning for future financial needs, or evaluating the long-term costs versus benefits of decisions in both personal finance and business scenarios.