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 ordinary annuity of $1:
$$\begin{array} { | c | c | c | c | c | c | }
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 4.452 & 4.329 & 4.212 & 4.100 & 3.993 \
\hline 6 & 5.242 & 5.076 & 4.917 & 4.767 & 4.623 \
\hline 7 & 6.002 & 5.786 & 5.582 & 5.389 & 5.206 \
\hline 8 & 6.733 & 6.463 & 6.210 & 5.971 & 5.747 \
\hline 9 & 7.435 & 7.108 & 6.802 & 6.515 & 6.247 \
\hline 10 & 8.111 & 7.722 & 7.360 & 7.024 & 6.710 \
\hline
\end{array}$$

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 ordinary annuity of $1:
$$\begin{array} { | c | c | c | c | c | c | } 
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 4.452 & 4.329 & 4.212 & 4.100 & 3.993 \
\hline 6 & 5.242 & 5.076 & 4.917 & 4.767 & 4.623 \
\hline 7 & 6.002 & 5.786 & 5.582 & 5.389 & 5.206 \
\hline 8 & 6.733 & 6.463 & 6.210 & 5.971 & 5.747 \
\hline 9 & 7.435 & 7.108 & 6.802 & 6.515 & 6.247 \
\hline 10 & 8.111 & 7.722 & 7.360 & 7.024 & 6.710 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The present value of the bonds at issuance is calculated by finding the present value of the principal (face value) and the present value of the interest payments. The bond pays interest semiannually, so the market rate per period is 4% (8% annual rate divided by 2), and there are 10 periods (5 years times 2). The face value is $71,000, and the semiannual interest payment is $2,485 ($71,000 * 7% / 2). Using the tables:1. Present value of the principal = $71,000 * 0.463 (from the present value of $1 table for 8% and 10 periods) = $32,873.2. Present value of the interest payments = $2,485 * 6.710 (from the present value of an ordinary annuity of $1 table for 8% and 10 periods) = $16,670.Adding these two amounts gives the total present value of the bond at issuance: $32,873 (principal) + $16,670 (interest) = $49,543. The correct answer is not listed, indicating a possible mistake in the calculation or in the provided options. However, based on the closest match to the correct process, C would be selected if it were a calculation based on correct principles and options provided.

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