The face value is $82,000, the stated rate is 10%, and the term of the bond is eight years. The bond pays interest semiannually. At the time of issue, the market rate is 8%. What is the present value of the bond at the issue date? Present value of $1:
$$\begin{array} { | l | l | l | l | l | l | }
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 15 & 0.555 & 0.481 & 0.417 & 0.362 & 0.315 \
\hline 16 & 0.534 & 0.458 & 0.394 & 0.339 & 0.292 \
\hline 17 & 0.513 & 0.436 & 0.371 & 0.317 & 0.270 \
\hline 18 & 0.494 & 0.416 & 0.350 & 0.296 & 0.250 \
\hline 19 & 0.475 & 0.396 & 0.331 & 0.277 & 0.232 \
\hline
\end{array}$$ Present value of ordinary annuity of $1:
$$\begin{array} { | r | c | c | c | c | c | }
\hline & 4 \% & 5 \% & 6 \% & { 7 \% } & 8 \% \
\hline 15 & 11.118 & 10.380 & 9.712 & 9.108 & 8.559 \
\hline 16 & 11.652 & 10.838 & 10.106 & 9.447 & 8.851 \
\hline 17 & 12.166 & 11.274 & 10.477 & 9.763 & 9.122 \
\hline 18 & 12.659 & 11.690 & 10.828 & 10.059 & 9.372 \
\hline 19 & 13.134 & 12.085 & 11.158 & 10.336 & 9.604 \
\hline
\end{array}$$

Question

The face value is $82,000, the stated rate is 10%, and the term of the bond is eight years. The bond pays interest semiannually. At the time of issue, the market rate is 8%. What is the present value of the bond at the issue date? Present value of $1:
$$\begin{array} { | l | l | l | l | l | l | } 
\hline & 4 \% & 5 \% & 6 \% & 7 \% & 8 \% \
\hline 15 & 0.555 & 0.481 & 0.417 & 0.362 & 0.315 \
\hline 16 & 0.534 & 0.458 & 0.394 & 0.339 & 0.292 \
\hline 17 & 0.513 & 0.436 & 0.371 & 0.317 & 0.270 \
\hline 18 & 0.494 & 0.416 & 0.350 & 0.296 & 0.250 \
\hline 19 & 0.475 & 0.396 & 0.331 & 0.277 & 0.232 \
\hline
\end{array}$$ Present value of ordinary annuity of $1:
$$\begin{array} { | r | c | c | c | c | c | } 
\hline & 4 \% & 5 \% & 6 \% &  { 7 \% } & 8 \% \
\hline 15 & 11.118 & 10.380 & 9.712 & 9.108 & 8.559 \
\hline 16 & 11.652 & 10.838 & 10.106 & 9.447 & 8.851 \
\hline 17 & 12.166 & 11.274 & 10.477 & 9.763 & 9.122 \
\hline 18 & 12.659 & 11.690 & 10.828 & 10.059 & 9.372 \
\hline 19 & 13.134 & 12.085 & 11.158 & 10.336 & 9.604 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The bond pays interest semiannually, so the market rate per period is 4% (8% annual rate / 2). The bond pays $4,100 every six months (10% of $82,000 / 2). The present value of the annuity (interest payments) is $4,100 * 12.659 (PV factor for 18 periods at 4%) = $51,901.90. The present value of the face value is $82,000 * 0.494 (PV factor for 18 periods at 4%) = $40,560. The total present value is $51,901.90 + $40,560 = $92,461.90, which rounds to $91,561.

The Face Value Is $82,000, the Stated Rate Is 10