John Doe wins the lottery and may pick from the following three choices:
Take $750,000 now.
Take $1,000,000 ten years from now.
Take $90,000 at the end of this year, and at the end of each following year for ten installments
In total.
Assume that John Doe uses a discount rate of 5% to evaluate his choices. If he selects the third option, how much is the present value of that alternative?
$\begin{array}{|c|c|c|c|c|c|c|}
\hline \text {Present}\
\text {Value of}\
\text {an}\
\text {Annuity of}\
\$ 1\
\hline&5\%&6\%&7\%&8\%&9\%&10\%\
\hline 1& 0.952 & 0.943 & 0.931 & 0.926 & 0.917 & 0.909 \
\hline2 & 1.859 & 1.833 & 1.808 & 1.783 & 1.759 &1.736 \
\hline 3& 2.723 & 2.673 & 2.624 & 2.577 & 2.531 &2.487 \
\hline 4& 3.546 & 3.465 & 3.387 & 3.312 & 3.240 &3.170 \
\hline5 & 4.329 & 4.21 & 4.100 & 3.993 & 3.890 &3.791 \
\hline6 & 5.076 & 4.917 & 4.767 & 4.623 & 4.486&4.355 \
\hline7 & 5.786 & 5.581 & 5.389 & 5.206 & 5.033 &4.868 \
\hline 8& 6.463 & 6.210 & 5.971 & 5.747 & 5.535 &5.335 \
\hline 9 & 7.108 & 6.80 & 6.515 & 6.247 & 5.995 &5.759 \
\hline 10& 7.722 & 7.360 &
7.024 & 6.710 & 6.418 &6.145 \
\hline
\end{array}$

Question

John Doe wins the lottery and may pick from the following three choices:
Take $750,000 now.
Take $1,000,000 ten years from now.
Take $90,000 at the end of this year, and at the end of each following year for ten installments
In total.
Assume that John Doe uses a discount rate of 5% to evaluate his choices. If he selects the third option, how much is the present value of that alternative?
$\begin{array}{|c|c|c|c|c|c|c|}
\hline \text {Present}\
\text {Value of}\
\text {an}\
\text {Annuity of}\
\$ 1\
\hline&5\%&6\%&7\%&8\%&9\%&10\%\
\hline 1& 0.952 & 0.943 & 0.931 & 0.926 & 0.917 & 0.909 \
\hline2 & 1.859 & 1.833 & 1.808 & 1.783 & 1.759 &1.736 \
\hline 3& 2.723 & 2.673 & 2.624 & 2.577 & 2.531 &2.487 \
\hline 4& 3.546 & 3.465 & 3.387 & 3.312 & 3.240 &3.170 \
\hline5 & 4.329 & 4.21 & 4.100 & 3.993 & 3.890 &3.791 \
\hline6 & 5.076 & 4.917 & 4.767 & 4.623 & 4.486&4.355 \
\hline7 & 5.786 & 5.581 & 5.389 & 5.206 & 5.033 &4.868 \
\hline 8& 6.463 & 6.210 & 5.971 & 5.747 & 5.535 &5.335 \
\hline 9 & 7.108 & 6.80 & 6.515 & 6.247 & 5.995 &5.759 \
\hline 10& 7.722 & 7.360 &
7.024  & 6.710 & 6.418 &6.145 \
\hline
\end{array}$

Quizplus · Accepted Answer

The present value of the annuity is calculated by multiplying the annual payment ($90,000) by the present value annuity factor for 10 years at 5%, which is 7.722. Thus, $90,000 * 7.722 = $694,980.

John Doe Wins the Lottery and May Pick from the Following