Which statement correctly describes the discount factor?

Which statement correctly describes the discount factor?

• A. Present Value equals FV divided by (1+r)^n
• B. Discount Factor equals FV
• C. Discount Factor equals 1/(1+r)^n
• D. Present Value equals FV times (1+r)^n

Answer: (C)

The discount factor is the factor you multiply a future amount by to convert it to present value. It depends on the rate per period and the number of periods, and it is defined as 1/(1+r)^n. Using this, the present value of a future value is PV = FV × DF = FV × 1/(1+r)^n, which is the same as PV = FV/(1+r)^n. That shows why the statement defining the discount factor as 1/(1+r)^n is the correct description. The idea is that discounting reduces value over time, so the factor is a fraction less than 1. The other forms either mix up the role of the factor or imply growth rather than discounting, such as present value equaling future value times (1+r)^n.

The discount factor is the factor you multiply a future amount by to convert it to present value. It depends on the rate per period and the number of periods, and it is defined as 1/(1+r)^n. Using this, the present value of a future value is PV = FV × DF = FV × 1/(1+r)^n, which is the same as PV = FV/(1+r)^n. That shows why the statement defining the discount factor as 1/(1+r)^n is the correct description. The idea is that discounting reduces value over time, so the factor is a fraction less than 1. The other forms either mix up the role of the factor or imply growth rather than discounting, such as present value equaling future value times (1+r)^n.