Bond value and changing required returns Midland Utilities has a bond issue outstanding that will mature to its $$1,000$ par value in $14$ years. The bond has a coupon interest rate of $9\%$ and pays interest annually.

a$.$ Find the bond value if the required return is $(1)9\%,(2)13\%,$ and $(3)6\%.$

b$.$ Use your finding in part a and the graph here, $\sqrt[\phantom{2}]{N},$ to discuss the relationship between the coupon rate, the required return and the market value of the bond relative to its par value.

c$.$ What two possible reasons could cause the required return to differ from the coupon interest rate?

a$.(1)$ The value of the bond, if the required retum is $9\%,$ is $ $($Round to the nearest cent.$)$