$1.$ Calculate the requested measures for bonds A and B $($assume that each bond pays coupon annually and the YTM compounds annually$)$ A$$ B $$ Coupon$8\%9\%$ YTM$8\%8\%$ Maturity$25$ Par$$ $$100$ $$100$ a$)$ Macaulay Duration b$)$ Modified Duration c$)$ Convexity Measure $1.$ Calculate the requested measures for bonds A and B $($assume that each bond pays coupon annually and the YTM compounds annually$)$

a$)$ Macaulay Duration

b$)$ Modified Duration

c$)$ Convexity Measure $2.$ For bond A and B in the previous question:

a$)$ Calculate the actual price of the bonds for a $\backslash (1\backslash \%\backslash )$ increase in interest rates.

b$)$ Using modified duration, estimate the price of the bonds for a $\backslash (1\backslash \%\backslash )$ increase in the interest rates

c$)$ Using both modified duration and convexity measure, estimate the price of the bonds for a $\backslash (1\backslash \%\backslash )$ increase in the interest rates

d$)$ Comment on the accuracy of your results in parts $($b$)$ and $($c$),$ and state why one approximation is closer to the actual price than the other

e$)$ Without working through calculations, indicate whether the duration of the two bonds would be higher or lower if the yield to maturity is $\backslash (10\backslash \%\backslash )$ rather than $8\backslash \%$