객관식
Which one of the following variables is the exponent in the present value formula \(PV = \dfrac{FV}{(1 + r)^n}\)?
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10. Time Value of Money
Time Value of Money Equations
객관식
Which of the following will increase the present value of an annuity, assuming all other factors remain constant?
A
Decreasing the number of periods
B
Increasing the discount rate
C
Decreasing the amount of each payment
D
Decreasing the discount rate
검증된 단계별 안내1
Understand the concept of present value of an annuity: The present value of an annuity is the current worth of a series of future payments, discounted at a specific rate. It is influenced by factors such as the number of periods, the discount rate, and the payment amount.
Recall the formula for the present value of an annuity: \( PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \), where \( PV \) is the present value, \( P \) is the payment amount, \( r \) is the discount rate per period, and \( n \) is the number of periods.
Analyze the impact of decreasing the discount rate: A lower discount rate \( r \) reduces the denominator in the formula, making the fraction larger. This increases the present value of the annuity because future payments are discounted less heavily.
Compare the other options: Decreasing the number of periods \( n \) reduces the total number of payments, which decreases the present value. Increasing the discount rate \( r \) increases the denominator, reducing the present value. Decreasing the payment amount \( P \) directly reduces the present value.
Conclude that decreasing the discount rate increases the present value of an annuity, as future payments are discounted less, making their present value higher.
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