Question $\backslash$#$6$: Yield$-$to$-$Maturity $[14$ Points$]$

Consider various U$.$S$.$ Treasury bonds that each pay a $\backslash (3\mathrm{.}8\backslash \%\backslash )$ annual coupon rate and have a face value of $\backslash (\backslash$$ $1000\backslash ).$

$($a$)$ Complete the table below. Show your work. $[6$ Points$]$

$($b$)$ Based on the table in Part $($a$),$ describe the relationship between current bond price and yieldto maturity. $[2$ Points$]$

$($c$)$ Consider various U$.$S$.$ Treasury bonds that each pay a $\backslash (3\mathrm{.}8\backslash \%\backslash )$ annual coupon rate and have a face value of $\backslash (\backslash$$ $1000\backslash ).$ Complete the table below. Show your work. $[6$ Points$]$

$($d$)$ Based on the table in Part $($c$),$ describe the relationship between years to maturity and the current bond price. $[2$ Points$]$

Question $\backslash$#$7$: Rate of Return $[10$ Points$]$

Suppose you purchased a $\backslash (\backslash$$ $1000\backslash )$ face value coupon bond with $14$ years to maturity for $\backslash (\backslash$$ $914\mathrm{.}64\backslash )$ today. It pays an annual coupon of $\backslash (\backslash$$ $61\backslash )$ per year.

$($a$)$ Calculate the current yield. $[2$ Points$]$

$($b$)$ Suppose after one year after purchasing the bond you decide to sell it$.$ Suppose that the yield to maturity is now $\backslash (5\mathrm{.}8\backslash \%\backslash ).$ What is the rate of return that you earned for holding the bond for one year $[$Hint: You'll need to solve for the price of the bond next year when you sell it$.$ Also $1$ year has passed since you purchased the bond.$][8$ Points$]$

Question $\backslash$#$8$: Consol $[3$ Points$]$

Calculate the yield$-$to$-$maturity of a consol selling for a price of $\backslash$$$920,$ a current yield of $3\mathrm{.}33\backslash \%$ and a face value of $\backslash (\backslash$$ $1000\backslash ).$