The face value of a bond is $71,000,its stated rate is 7%,and the term of the bond is five years.The bond pays interest semiannually.At the time of issue,the market rate is 8%.Determine the present value of the bonds at issuance. Present value of $1:
$$\begin{array} { | c | l | l | l | l | l | }
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 0.822 & 0.784 & 0.747 & 0.713 & 0.681 \
\hline 6 & 0.790 & 0.746 & 0.705 & 0.666 & 0.630 \
\hline 7 & 0.760 & 0.711 & 0.665 & 0.623 & 0.583 \
\hline 8 & 0.731 & 0.677 & 0.627 & 0.582 & 0.540 \
\hline 9 & 0.703 & 0.645 & 0.592 & 0.544 & 0.500 \
\hline 10 & 0.676 & 0.614 & 0.558 & 0.508 & 0.463 \
\hline
\end{array}$$ Present value of annuity of $1:
$$\begin{array} { | c | l | l | l | l | l | }
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 4.452 & 4.329 & 4.212 & 4.100 & 3.993 \
\hline 6 & 5.242 & 5.076 & 4.917 & 4.767 & 4.623 \
\hline 7 & 6.002 & 5.786 & 5.582 & 5.389 & 5.206 \
\hline 8 & 6.733 & 6.463 & 6.210 & 5.971 & 5.747 \
\hline 9 & 7.435 & 7.108 & 6.802 & 6.515 & 6.247 \
\hline 10 & 8.111 & 7.722 & 7.360 & 7.024 & 6.710 \
\hline
\end{array}$$

Question

The face value of a bond is $71,000,its stated rate is 7%,and the term of the bond is five years.The bond pays interest semiannually.At the time of issue,the market rate is 8%.Determine the present value of the bonds at issuance. Present value of $1:
$$\begin{array} { | c | l | l | l | l | l | } 
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 0.822 & 0.784 & 0.747 & 0.713 & 0.681 \
\hline 6 & 0.790 & 0.746 & 0.705 & 0.666 & 0.630 \
\hline 7 & 0.760 & 0.711 & 0.665 & 0.623 & 0.583 \
\hline 8 & 0.731 & 0.677 & 0.627 & 0.582 & 0.540 \
\hline 9 & 0.703 & 0.645 & 0.592 & 0.544 & 0.500 \
\hline 10 & 0.676 & 0.614 & 0.558 & 0.508 & 0.463 \
\hline
\end{array}$$ Present value of annuity of $1:
$$\begin{array} { | c | l | l | l | l | l | } 
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 4.452 & 4.329 & 4.212 & 4.100 & 3.993 \
\hline 6 & 5.242 & 5.076 & 4.917 & 4.767 & 4.623 \
\hline 7 & 6.002 & 5.786 & 5.582 & 5.389 & 5.206 \
\hline 8 & 6.733 & 6.463 & 6.210 & 5.971 & 5.747 \
\hline 9 & 7.435 & 7.108 & 6.802 & 6.515 & 6.247 \
\hline 10 & 8.111 & 7.722 & 7.360 & 7.024 & 6.710 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The bond pays interest semiannually, so the market rate is 4% per period (8% annually divided by 2), and there are 10 periods (5 years times 2). The semiannual interest payment is $2,485 ($71,000 * 7% / 2). The present value of the interest payments is $11,507.55 ($2,485 * 4.623), and the present value of the face value is $43,235 ($71,000 * 0.608). Adding these gives a total present value of $68,152.55, rounded to $68,152.

The Face Value of a Bond Is $71,000,its Stated Rate