Question

Your aunt offers you a choice of \(20,100 in 20 years or \)870 today. If money is discounted at 17 percent, which should you choose?

Short answer

An individual should be indifferent between the two choices because the present value of both the options is the same.

Step-by-step solution

Identification of the required information

Future value (FV) = $20,100

Interest Rate (i) = 17%

Period (n) = 20 year

Present value (PV)

$$\begin{gathered} \text{PV}\mathbf{=}\text{FV}\times {\left(1+i\right)}^{-n} \\ \mathbf{=}\$20,100\times {\left(1+17\%\right)}^{-20} \\ \mathbf{=}\$869.92 \end{gathered}$$

Final decision

The present value of $20,100 in 20 years is $869,92 which is almost equal to $870 today. Thus, an individual should be indifferent between the options.