Q$\mathrm{.}3)$ Suppose you purchase a five$-$year, $7$ percent coupon bond $($paid annually$)$ that is priced to yield $8$ percent. The face value of the bond is $$1,500.(25$ marks$)$a$.$ Show that the duration of this bond is equal to four years. Salek D$9$b$.$ Show that if interest rates rise to & percent within the next year and your investment horizon is four years from today, you will still earn an $8$ percent yield on your investment.c$.$ Show that an $8$ percent yield also will be earned if interest rates fall next year to $7$ percent.