Please show work.

Consider a bond selling at par $($$$1000)$ with a coupon rate of $6\%$ and $10$ years to maturity. $($Assuming

semi$-$annual coupon payments$)$

$($a$)$ What is the price of this bond if the required yield is $8\%?$

$($b$)$ What is the price of this bond if the required yield increases from $8\%$ to $9\%,$ and by what

percentage

did the price of this bond change?

Twitchy $-$ a kind of junk bond $-$ carries a $10\%$ coupon rate, has a $$1,000$ face value and matures in $5$

years. What is the change in the implicit required return $($that is$,$ YTM$)$ of Twitchy, if the current

market price of Twitchy, which is $$950,$ falls to $$850?$

a$.-4\mathrm{.}10\%$

b$.+2\mathrm{.}96\%$

c$.+11\mathrm{.}34\%$

d$.-14\mathrm{.}30\%$

Consider a bond with a $10\%$ coupon rate and a yield to maturity of $8\%.$ If the bond's YTM

remains constant, then in one year, the bond price will be $($higher$,$ lower$)$ because this is a

$($discount$,$ premium$)$ bond.

a$.$ higher, premium

b$.$ higher, discount

c$.$ lower, premium

d$.$ lower, discount

Which bond would most likely possess the highest degree of interest rate risk?

a$.8\%$ coupon rate, $10$ years to maturity

b$.8\%$ coupon rate, $20$ years to maturity

c$.10\%$ coupon rate, $10$ years to maturity

d$.10\%$ coupon rate, $20$ years to maturity