Congratulations! You just won $$150,000$ in the state lottery. You can collect

$$15,000$ today and receive the remainder in annual payments of the same amount $($i$.$e$.,$ also

$$15,000).$ Or you can take a lump$-$sum payment of $$125,000$ today. Which should you choose? Use the current U$.$S$.$ Treasury $10-$Year Note yield $(4\mathrm{.}50\%)$ as your discount rate to calculate the PV of the annuity. What is the PV if your payments increase by $2\%$ per year? Why is the U$.$S$.$

$10-$Year Note yield an appropriate discount rate? Or is it$?$ What is your opportunity cost?