Calculate the fair present values of the following bonds, all of which pay interest semiannually, have a face value of $$1,000,$ have $20$ years remaining to maturity, and have a required rate of return of $10$ percent.

a$.$ The bond has a $6$ percent coupon rate.

b$.$ The bond has a $8$ percent coupon rate.

C$.$ The bond has a $10$ percent coupon rate.

d$.$ What do your answers to parts $($a$)$ through $($c$)$ say about the relation between coupon rates and present values?