$(17$ points total$)$ Suppose you own $$100$ par of a $10-$year bond that pays semi$-$annually with

an $($annualized$)$ coupon of $5\%.$ The market interest rate, $R,$ is $4\%($also annualized$).$

a$)$ Calculate the PV$,$ Macauley Duration and Modified Duration $(9$ points$)$

b$)$ Suppose the market interest rate increases by $1\mathrm{.}5\%.$ Calculate $\frac{P}{P}$ and $P(8$ points$)$

Note: you must build a table and not use Excel bond or interest rate functions.