Lahey Industries has an outstanding $$1,000$ par$-$value bond with an $8\%$ coupon rate. The bond has $12$ years remaining to its maturity date.

a$.$ If interest is paid annually, find the value of the bond when the required return is: $(1)7\%,(2)8\%,(3)10\%.$

b$.$ Indicate for each case in part $($a$)$ whether the bond is selling at a discount, at premium or at its par value.

c$.$ Using the $10\%$ required return, find the bond's value when interest is paid semi$-$annually.