Question

Your father offers you a choice of $105,000in12yearsor$47,000 today. a. If money is discounted at 8 percent, which should you choose?

Short answer

The choice of $47,000 today should be preferred over $105,000 in 12 years.

Step-by-step solution

Identification of the required information

Future value (FV) = $105,000

Interest Rate (i) = 8%

Period (n) = 12 year

Present value (PV)

$$\begin{gathered} \mathbf{\text{PV}}\mathbf{=}\mathbf{\text{FV}}\mathbf{\times }{\left(1+i\right)}^{\mathbf{-}\mathbf{n}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{105}\mathbf{,}\mathbf{000}\mathbf{\times }{\left(1+8\%\right)}^{\mathbf{-}\mathbf{12}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{41}\mathbf{,}\mathbf{696}\mathbf{.}\mathbf{94} \end{gathered}$$

Final decision

The present value of $105,000 in 12 years is $41,696.94 which is lower than $47,000 today. Thus, the option of $47,000 today should be chosen.