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Multiple Choice
Which of the following is true about perpetuities?
A
Perpetuities are only used to value stocks with growing dividends.
B
A perpetuity has a fixed maturity date.
C
The present value of a perpetuity is calculated using the formula \(PV = FV \times (1 + r)^n\).
D
A perpetuity pays a fixed amount at regular intervals forever.
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Verified step by step guidance
1
Understand the concept of a perpetuity: A perpetuity is a financial instrument that pays a fixed amount at regular intervals indefinitely, meaning it has no end date.
Clarify the incorrect options: Perpetuities are not limited to valuing stocks with growing dividends; they can be used in various financial contexts. Additionally, a perpetuity does not have a fixed maturity date, as it continues forever.
Analyze the formula provided: The formula \(PV = FV \times (1 + r)^n\) is incorrect for perpetuities. This formula is used for calculating the future value of a lump sum or an annuity, not for perpetuities.
Learn the correct formula for the present value of a perpetuity: The present value of a perpetuity is calculated using the formula \(PV = \frac{C}{r}\), where \(C\) is the fixed payment amount, and \(r\) is the discount rate.
Conclude with the correct statement: The correct answer is that a perpetuity pays a fixed amount at regular intervals forever, which aligns with the definition of a perpetuity.