Consider a $7-$year Treasury Strip with face value $$1,000.$

$($a$)$ What is the bond price if the required rate of return is $6\%$ with annual compounding?

$($b$)$ True or false? If the required rate of return increases, the bond price increases all else equal. Justify your answer.

$($c$)$ What is the bond price if the required rate of return is $6\%$ with monthly compounding?