Juan has just received a prize which entitles him to receive annual payments of $10,000 at the end of each year for the next 10 years. He would like to sell the rights to the prize money to a financial institution, so that he can have the cash now. In order to estimate the present value of the prize, he will use a discount rate of 5%. What is the present value of the prize?
$\begin{array}{|r|c|c|c|c|c|c|}
\hline \text {Present Value of }\
\text {an Annuity of \$ 1}\
\hline &5\%&6\%&7\%&8\%&9\%&10\%\
\hline1 & 0.952 & 0.943 & 0.935 & 0.926 & 0.917 & 0.909 \
\hline 2& 1.859 & 1.833 & 1.808 & 1.783 & 1.759 & 1.736 \
\hline 3& 2.723 & 2.673 & 2.624 & 2.577 & 2.531 & 2.487 \
\hline 4 & 3.546 & 3.465 & 3.387 & 3.312 & 3.240 & 3.170 \
\hline 5& 4.329 & 4.212 & 4.100 & 3.993 & 3.890 & 3.791 \
\hline6& 5.076 & 4.917 & 4.767 & 4.623 & 4.486&4.355 \
\hline7& 5.786& 5.582 & 5.389 & 5.206 & 5.033&4.868 \
\hline8& 6.463 & 6.210 & 5.971 & 5.747 & 5.535&5.335 \
\hline9& 7.108 & 6.802 & 6.515 & 6.247 & 5.995&5.759\
\hline 10&7.722& 7.360 & 7.024 & 6.710&6.418&6.145 \
\hline
\end{array}$

Question

Juan has just received a prize which entitles him to receive annual payments of $10,000 at the end of each year for the next 10 years. He would like to sell the rights to the prize money to a financial institution, so that he can have the cash now. In order to estimate the present value of the prize, he will use a discount rate of 5%. What is the present value of the prize?
$\begin{array}{|r|c|c|c|c|c|c|}
\hline \text {Present Value of  }\
\text {an Annuity of \$ 1}\
\hline &5\%&6\%&7\%&8\%&9\%&10\%\
\hline1 & 0.952 & 0.943 & 0.935 & 0.926 & 0.917 & 0.909 \
\hline 2& 1.859 & 1.833 & 1.808 & 1.783 & 1.759 & 1.736 \
\hline 3& 2.723 & 2.673 & 2.624 & 2.577 & 2.531 & 2.487 \
\hline 4 & 3.546 & 3.465 & 3.387 & 3.312 & 3.240 & 3.170 \
\hline 5& 4.329 & 4.212 & 4.100 & 3.993 & 3.890 & 3.791 \
\hline6& 5.076 & 4.917 & 4.767 & 4.623 & 4.486&4.355 \
\hline7& 5.786& 5.582 & 5.389 & 5.206 & 5.033&4.868 \
\hline8& 6.463 & 6.210 & 5.971 & 5.747 & 5.535&5.335 \
\hline9& 7.108 & 6.802 & 6.515 & 6.247 & 5.995&5.759\
\hline 10&7.722& 7.360 & 7.024 & 6.710&6.418&6.145 \
\hline
\end{array}$

Quizplus · Accepted Answer

The present value of the annuity can be calculated by multiplying the annual payment ($10,000) by the present value factor for a 10-year annuity at a 5% discount rate, which is 7.722. Therefore, the present value is $10,000 * 7.722 = $77,220.

Juan Has Just Received a Prize Which Entitles Him to Receive