Consider the case of a fixed$-$coupon bond. The coupon rate is denoted by $c,$ whereas the interest rate is constant and given by $r>0.$ The face value of the bond is $F,$ which is paid at the end of year $n.$ At the end of each year $y=1,$dots,$n,$ the bond pays a single coupon with total value of $C=cF.$ Based on this information, what is the price of this bond at time $0,$ i$.$e$.,$ what is $V(0)?$ Your answer should demonstrate the steps needed to come up with the closed$-$form $($analytical$)$ solution.

Consider a special case of $c=r.$ What is $V(0)?$

Suppose one year passes and the interest rate stays the same. What is the price of the bond at $y=1,$ i$.$e$.,V(1)?$

Related to the previous part, how does $V(1)$ compare with $V(0)?$ Show the condition for which $V(0)>V(1)$ holds.