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

question 191

Multiple Choice

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:
$$\begin{array} { | r | c | c | r | r | r | } \hline & 4 \% & 5 \% &{ 6 \% } & { 7 \% } & 8 \% \\\hline 15 & 11.118 & 10.380 & 9.712 & 9.108 & 8.559 \\\hline 16 & 11.652 & 10.838 & 10.106 & 9.447 & 8.851 \\\hline 17 & 12.166 & 11.274 & 10.477 & 9.763 & 9.122 \\\hline 18 & 12.659 & 11.690 & 10.828 & 10.059 & 9.372 \\\hline 19 & 13.134 & 12.085 & 11.158 & 10.336 & 9.604 \\\hline\end{array}$$

• A) $91,561
• B) $47,773
• C) $43,673
• D) $84,788

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Definitions:

Normal Random Variable

A normal random variable is a variable whose values are distributed according to the normal distribution, characterized by its mean and standard deviation.

Standard Deviation

A statistic that measures the dispersion or variability of a dataset relative to its mean, indicating how spread out the numbers are.

Normally Distributed

Refers to a type of distribution where the data points are symmetrically distributed around the mean, with most observations clustering around the central peak and the probabilities for values further from the mean tapering off equally in both directions.

Mean

The mean of a collection of numbers, determined by dividing their total sum by the count of the numbers.