A $25$ year bond pays $9\%$ coupon and has a face value of $$100.$ Suppose the initial yield is $9\%.$ A$)$ Calculate the price of the bond. B$)$ Approximate the price change due to duration of a change in yield to $7\%.$ C$)$ If the bond as originally described had a shorter time to maturity than $25$ years, how would you answer question b$)$ change and what is reason?