$($Bond valuation$)$ You own a bond that pays $$120$ in annual interest, with a $$1,000$ par value. It matures in $20$ years. Your required rate of return is $10$

percent.

a$.$ Calculate the value of the bond.

b$.$ How does the value change if your required rate of return $(1)$ increases to $15$ percent or $(2)$ decreases to $6$ percent?

c$.$ Explain the implications of your answers in part $b$ as they relate to interest rate risk, premium bonds, and discount bonds.

d$.$ Assume that the bond matures in $3$ years instead of $20$ years. Recompute your answers in part $b.$

e$.$ Explain the implications of your answers in part $d$ as they relate to interest rate risk, premium bonds, and discount bonds.

a$.$ If your required rate of return is $10$ percent, what is the value of the bond?

$($Round to the nearest cent.$)$