Peter Smith has just won the state lottery and has the following three payout options for after-tax prize money: 1.$50,000 per year at the end of each of the next six years
2)$300,000 (lump sum)now
3)$510,000 (lump sum)six years from now
The annual discount rate is 9%.Compute the present value of the third option.(Round to nearest whole dollar.)
Present value of $1:
$$\begin{array} { | l | r | r | r | }
\hline & 8 \% & 9 \% & 10 \% \
\hline 1 & 0.926 & 0.917 & 0.909 \
\hline 2 & 0.857 & 0.842 & 0.826 \
\hline 3 & 0.794 & 0.772 & 0.751 \
\hline 4 & 0.735 & 0.708 & 0.683 \
\hline 5 & 0.681 & 0.650 & 0.621 \
\hline 6 & 0.630 & 0.596 & 0.564 \
\hline 7 & 0.583 & 0.547 & 0.513 \
\hline
\end{array}$$

Question

Peter Smith has just won the state lottery and has the following three payout options for after-tax prize money: 1.$50,000 per year at the end of each of the next six years
2)$300,000 (lump sum)now
3)$510,000 (lump sum)six years from now
The annual discount rate is 9%.Compute the present value of the third option.(Round to nearest whole dollar.)
Present value of $1:
$$\begin{array} { | l | r | r | r | } 
\hline & 8 \% & 9 \% & 10 \% \
\hline 1 & 0.926 & 0.917 & 0.909 \
\hline 2 & 0.857 & 0.842 & 0.826 \
\hline 3 & 0.794 & 0.772 & 0.751 \
\hline 4 & 0.735 & 0.708 & 0.683 \
\hline 5 & 0.681 & 0.650 & 0.621 \
\hline 6 & 0.630 & 0.596 & 0.564 \
\hline 7 & 0.583 & 0.547 & 0.513 \
\hline
\end{array}$$

Quizplus · Accepted Answer

To calculate the present value of the third option ($510,000 in six years), we use the present value formula: PV = FV / (1 + r)^n, where FV is the future value, r is the annual discount rate, and n is the number of years. Using the table provided for a 9% discount rate over 6 years, the present value factor is 0.596. Therefore, the present value is $510,000 * 0.596 = $303,960 (rounded to the nearest whole dollar).

Peter Smith Has Just Won the State Lottery and Has