An investment today of $8,424 at 6% will yield $2,000 per year for the next five years because interest is being earned on principal that is left invested each year. The following tables are available:
Present value of $1:
$$\begin{array} { | l | c | c | c | c | c | }
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 0.822 & 0.784 & 0.747 & 0.713 & 0.681 \
\hline 6 & 0.790 & 0.746 & 0.705 & 0.666 & 0.630 \
\hline 7& 0.760 & 0.711 & 0.665 & 0.623 & 0.583 \
\hline 8& 0.731 & 0.677 & 0.627 & 0.582 & 0.540 \
\hline 9& 0.703 & 0.645 & 0.592 & 0.544 & 0.500 \
\hline 10 & 0.676 & 0.614 & 0.558 & 0.508 & 0.463 \
\hline
\end{array}$$ Present value of ordinary annuity of $1:
$$\begin{array} { | l | c | c | c | c | c | }
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 4.452 & 4.329 & 4.212 & 4.100 & 3.993 \
\hline 6 & 5.242 & 5.076 & 4.917 & 4.767 & 4.623 \
\hline7 & 6.002 & 5.786 & 5.582 & 5.389 & 5.206 \
\hline 8 & 6.733 & 6.463 & 6.210 & 5.971 & 5.747 \
\hline 9 & 7.435 & 7.108 & 6.802 & 6.515 & 6.247 \
\hline 10 & 8.111 & 7.722 & 7.360 & 7.024 & 6.710 \
\hline
\end{array}$$

Question

An investment today of $8,424 at 6% will yield $2,000 per year for the next five years because interest is being earned on principal that is left invested each year. The following tables are available:
Present value of $1:
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 0.822 & 0.784 & 0.747 & 0.713 & 0.681 \
\hline 6 & 0.790 & 0.746 & 0.705 & 0.666 & 0.630 \
 \hline 7& 0.760 & 0.711 & 0.665 & 0.623 & 0.583 \
 \hline 8& 0.731 & 0.677 & 0.627 & 0.582 & 0.540 \
 \hline 9& 0.703 & 0.645 & 0.592 & 0.544 & 0.500 \
\hline 10 & 0.676 & 0.614 & 0.558 & 0.508 & 0.463 \
\hline
\end{array}$$ Present value of ordinary annuity of $1:
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 4.452 & 4.329 & 4.212 & 4.100 & 3.993 \
\hline 6 & 5.242 & 5.076 & 4.917 & 4.767 & 4.623 \
 \hline7 & 6.002 & 5.786 & 5.582 & 5.389 & 5.206 \
\hline 8 & 6.733 & 6.463 & 6.210 & 5.971 & 5.747 \
\hline 9 & 7.435 & 7.108 & 6.802 & 6.515 & 6.247 \
\hline 10 & 8.111 & 7.722 & 7.360 & 7.024 & 6.710 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The problem involves calculating the present value of an annuity, which can be done using the present value of an ordinary annuity of $1 table. The initial investment of $8,424 is the present value of the annuity that will yield $2,000 per year for five years at a 6% interest rate. Using the present value of an ordinary annuity of $1 table, we can calculate that the present value of a five-year annuity that pays $1 per year at a 6% interest rate is 4.212. Therefore, the present value of a five-year annuity that pays $2,000 per year at a 6% interest rate is $8,424 * 4.212 = $35,429.68. This confirms that the investment today of $8,424 will yield $2,000 per year for the next five years.

An Investment Today of $8,424 at 6% Will Yield $2,000