$1.$ The RHR Corporation's $11\%$ coupon $($paid semiannually$)$ bonds mature in five years. The bonds' current yield to maturity is $12\%.$

a$.$ Calculate the Macaulay duration of the bonds.

b$.$ Calculate the modified duration of the bonds

c$.$ Assume that the bonds' YTM drops from $12\%$ to $11\mathrm{.}5\%.$ Calculate an estimate of the price change.

d$.$ Explain why modified duration is a better measure than maturity when calculating the bond's sensitivity to changes in interest rates.

e$.$ Identify the direction of change in modified duration if:

$(1)$ The coupon rate of the bond was $9\%$ rather than $11\%$

$(2)$ The maturity of the bond was $8$ years rather than $5$ years.

f$.$ Define convexity and explain how modified duration and convexity are used to approximate the bond's percentage change in price given a large change in interest rates. I need to answer those in excel. Thank you