Future value is best defined as:

Question

BlackTom AI · Accepted Answer

FV = PV × (1 + r)^n — future value is the present amount compounded forward by the interest rate for the number of periods.

1. Relevant knowledge and concepts
- Future value (FV): the value of a current asset at a specified date in the future based on an assumed rate of growth (interest).
- Present value (PV): today's value of a future sum discounted back.
- Compounding: applying interest repeatedly so that interest earns interest.
- Distinction from annuity and present-value concepts: periodic payments and discounting are different constructs.

2. Step-by-step reasoning
- The formal definition of future value: take an initial amount (PV) and grow it by interest each period. After one period: FV1 = PV(1 + r). After n periods: FVn = PV(1 + r)^n.
- This definition describes “the amount an investment is worth at the end of some stated period of time.” It directly matches the language of the choice.

3. Intermediate steps / formula demonstration
- Start with PV.
- Apply interest for one period: PV × (1 + r).
- Apply interest for a second period: PV × (1 + r) × (1 + r) = PV × (1 + r)^2.
- After n periods: FV = PV × (1 + r)^n. This shows how the present sum becomes the future amount.

4. Why the correct answer is correct
- The phrase “worth at the end of some stated period” captures compounding to a future date, which is precisely what future value measures. It does not discount to today’s dollars nor describe periodic payments.

5. Why other options are incorrect
- “An amount of money received each period…” describes an annuity (periodic cash flows), not FV of a lump sum.
- “The cash value of an investment in today's dollars…” and “The amount an investment is worth in today's dollars.” both describe present value, the discounted value.
- “The dollar amount invested today at a stated rate…” describes the present value or principal, not the future value.

6. Conclusion
The correct definition is “The amount an investment is worth at the end of some stated period of time,” which matches the provided answer.

Future value is best defined as:单项选择题

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