So$,$ why is it important to be able to calculate the future value of some amount invested?

LUKE: First, remember that the amount invested is usually called $,$ and the amount earned during the investment period is called $.$ It is important to be able to calculate a future value so that you can know in advance what a given amount of principal will be worth after earning a specified for a known $.$

LEXI: OK$,$ I understand that, and I know the amount of principal invested today can be called the value of the investment, whereas the amount realized after the passage of t period of time is called its value. But what causes the present and future values to be different values?

LUKE: Two things cause the present and future values to be different amounts. First, the earned during the investment period causes the future value to be greater than, equal to$,$ or less than the present value. Second, the method used to calculate the interest earned$$that is$,$ whether the account pays interest$$determines the amount by which the future value differs from the present value.

LEXI: That makes sense, and I remember Dr$.$ Phillips saying that the difference between simple and compound interest is that in the case of interest, interest is earned solely on the invested principal, but in the case of interest, interest is earned not only on the principal but also on previously earned interest.

LUKE: Very good! So$,$ here$$s your next question. Assuming equal amounts of principal, interest rates, and investment periods, which type of account should produce the greater future value: the account earning simple interest or the account earning compound interest?

LEXI: By my reasoning, the account earning interest should have the greater future value, assuming identical amounts of principal, interest rates, and investment periods.