Question

Rita Gonzales won the \(41 million lottery. She is to receive \)1.5 million a year for the next 19 years plus an additional lump sum payment of $12.5 million after 19 years. The discount rate is 14 percent. What is the current value of her winnings?

Short answer

The current value is $10,862,407.79.

Step-by-step solution

Identification of the required information

Payment (PMT) = $1,500,000

Future value (FV) = $12,500,000

Period (n) = 19 year

Interest Rate (i) = 14%

Current value (PV)

$$\begin{gathered} PV=PMT\times \left[\frac{1-{\left(1+i\right)}^{-n}}{i}\right]+FV\times {\left(1+i\right)}^{-n} \\ =\$1,500,000\times \left[\frac{1-{\left(1+14\%\right)}^{-19}}{14\%}\right]+\$12,500,000\times {\left(1+14\%\right)}^{-19} \\ =\$10,862,407.79 \end{gathered}$$