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:
$$\begin{array} { | c | l | l | l | l | l | }
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 4.452 & 4.329 & 4.212 & 4.100 & 3.993 \
\hline 6 & 5.242 & 5.076 & 4.917 & 4.767 & 4.623 \
\hline 7 & 6.002 & 5.786 & 5.582 & 5.389 & 5.206 \
\hline 8 & 6.733 & 6.463 & 6.210 & 5.971 & 5.747 \
\hline 9 & 7.435 & 7.108 & 6.802 & 6.515 & 6.247 \
\hline 10 & 8.111 & 7.722 & 7.360 & 7.024 & 6.710 \
\hline
\end{array}$$
A) $50,844
B) $20,156
C) $68,152
D) $71,000

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:
$$\begin{array} { | c | l | l | l | l | l | } 
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 5 & 4.452 & 4.329 & 4.212 & 4.100 & 3.993 \
\hline 6 & 5.242 & 5.076 & 4.917 & 4.767 & 4.623 \
\hline 7 & 6.002 & 5.786 & 5.582 & 5.389 & 5.206 \
\hline 8 & 6.733 & 6.463 & 6.210 & 5.971 & 5.747 \
\hline 9 & 7.435 & 7.108 & 6.802 & 6.515 & 6.247 \
\hline 10 & 8.111 & 7.722 & 7.360 & 7.024 & 6.710 \
\hline
\end{array}$$
A) $50,844
B) $20,156
C) $68,152
D) $71,000

Quizplus · Accepted Answer

The present value of the bond is calculated by adding the present value of the interest payments (an annuity) and the present value of the principal amount (a lump sum) at the end of the term. The interest payment per period is $71,000 * 7% / 2 = $2,485. Since the bond pays semiannually, there are 10 periods (5 years * 2). The market rate per period is 8% / 2 = 4%. Using the tables, the present value of the annuity (interest payments) is $2,485 * 8.111 (from the annuity table at 4% for 10 periods) = $20,156. The present value of the principal ($71,000) is $71,000 * 0.676 (from the $1 table at 4% for 10 periods) = $47,996. Adding these two amounts gives $20,156 + $47,996 = $68,152.

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