Question

You are going to receive $205,000 in 18 years. What is the difference in present value between using a discount rate of 12 percent versus 9 percent?

Short answer

The difference in present value is $16,800.60.

Step-by-step solution

Identification of the required information

Future value (FV) = $205,000

Period (n) = 18 year

Present value (PV) at Interest Rate (i) = 12%

$$\begin{gathered} \text{PV}\mathbf{=}\text{FV}\times {\left(1+i\right)}^{-n} \\ \mathbf{=}\$205,000\times {\left(1+12\%\right)}^{-18} \\ \mathbf{=}\$26,658.12 \end{gathered}$$

Present value (PV) at Interest Rate (i) = 9%

$$\begin{gathered} \text{PV}\mathbf{=}\text{FV}\times {\left(1+i\right)}^{-n} \\ \mathbf{=}\$205,000\times {\left(1+9\%\right)}^{-18} \\ \mathbf{=}\$43,458.72 \end{gathered}$$

Difference in present value

$$\begin{gathered} \text{Difference in PV}\mathbf{=}\text{PV at 9\% - PV at 12\%} \\ \mathbf{=}\$43,458.72-\$26,658.12 \\ \mathbf{=}\$16,800.60 \end{gathered}$$