Question

The Clearinghouse Sweepstakes has just informed you that you have won \(1 million. The amount is to be paid out at the rate of \)20,000 a year for the next 50 years. With a discount rate of 10 percent, what is the present value of your winnings?

Short answer

The present value is $198,296.29.

Step-by-step solution

Identification of the required information

Payment (PMT) = $20,000

Period (n) = 50 year

Interest Rate (i) = 10%

Present value (PV)

$$\begin{gathered} \text{PV}\mathbf{=}\text{PMT}\times \left[\frac{1-{\left(1+i\right)}^{-n}}{i}\right] \\ \mathbf{=}\$20,000\times \left[\frac{1-{\left(1+10\%\right)}^{-50}}{10\%}\right] \\ \mathbf{=}\$198,296.29 \end{gathered}$$