91Ó°ÊÓ

When the stated interest rate is equal to the market interest rate, these bonds are known as bonds issued at par.

$\begin{array}{c}\mathbf{C}\mathbf{o}\mathbf{u}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{=}\mathbf{P}\mathbf{a}\mathbf{r}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{×}\mathbf{C}\mathbf{o}\mathbf{u}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{R}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{×}\mathbf{T}\mathbf{i}\mathbf{m}\mathbf{e}\mathbf{P}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}\\ \mathbf{=}\mathbf{\$}\mathbf{83}\mathbf{,}\mathbf{000}\mathbf{×}\mathbf{10}\mathbf{\%}\mathbf{×}\frac{\mathbf{6}}{\mathbf{12}}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{150}\end{array}$

Calculation of discount allowed and interest expenses (part 2):

$\begin{array}{c}\mathbf{D}\mathbf{i}\mathbf{s}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{A}\mathbf{l}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{e}\mathbf{d}\mathbf{=}\mathbf{P}\mathbf{a}\mathbf{r}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{-}\mathbf{I}\mathbf{s}\mathbf{s}\mathbf{u}\mathbf{e}\mathbf{d}\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\\ \mathbf{=}\mathbf{\$}\mathbf{83}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{62}\mathbf{,}\mathbf{433}\\ \mathbf{=}\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{567}\end{array}$

$\begin{array}{c}\mathbf{D}\mathbf{i}\mathbf{s}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{O}\mathbf{n}\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{z}\mathbf{e}\mathbf{d}\mathbf{=}\mathbf{I}\mathbf{s}\mathbf{s}\mathbf{u}\mathbf{e}\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{×}\mathbf{I}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{R}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{×}\mathbf{P}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}\mathbf{-}\mathbf{C}\mathbf{o}\mathbf{u}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{\$}\mathbf{62}\mathbf{,}\mathbf{433}\mathbf{×}\mathbf{16}\mathbf{\%}\mathbf{×}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{-}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{150}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{995}\mathbf{-}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{150}\\ \mathbf{=}\mathbf{\$}\mathbf{845}\end{array}$

$\begin{array}{c}\mathbf{I}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{E}\mathbf{x}\mathbf{p}\mathbf{e}\mathbf{n}\mathbf{s}\mathbf{e}\mathbf{s}\mathbf{=}\mathbf{D}\mathbf{i}\mathbf{s}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{O}\mathbf{n}\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{z}\mathbf{e}\mathbf{d}\mathbf{+}\mathbf{C}\mathbf{o}\mathbf{u}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{\$}\mathbf{845}\mathbf{+}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{150}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{995}\end{array}$

Calculation of premium amount and interest expenses (part 3):

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{m}\mathbf{i}\mathbf{u}\mathbf{m}\mathbf{o}\mathbf{n}\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{=}\mathbf{I}\mathbf{s}\mathbf{s}\mathbf{u}\mathbf{e}\mathbf{d}\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{−}\mathbf{P}\mathbf{a}\mathbf{r}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\\ \mathbf{=}\mathbf{\$}\mathbf{91}\mathbf{,}\mathbf{727}\mathbf{-}\mathbf{\$}\mathbf{83}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{727}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{m}\mathbf{i}\mathbf{u}\mathbf{m}\mathbf{o}\mathbf{n}\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{z}\mathbf{e}\mathbf{d}\mathbf{=}\mathbf{C}\mathbf{o}\mathbf{u}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{I}\mathbf{s}\mathbf{s}\mathbf{u}\mathbf{e}\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{×}\mathbf{I}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{R}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{×}\mathbf{P}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{150}\mathbf{-}\mathbf{\$}\mathbf{91}\mathbf{,}\mathbf{727}\mathbf{×}\mathbf{8}\mathbf{\%}\mathbf{×}\frac{\mathbf{1}}{\mathbf{2}}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{150}\mathbf{-}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{670}\\ \mathbf{=}\mathbf{\$}\mathbf{480}\end{array}$

role="math" localid="1657181921662" $\begin{array}{c}\mathbf{InterestExpenses}\mathbf{=}\mathbf{CouponAmount}\mathbf{−}\mathbf{\text{Premium}}\mathbf{onBondAmortized}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{150}\mathbf{-}\mathbf{\$}\mathbf{480}\\ \mathbf{=}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{670}\end{array}$