$1.$ We have a bond with a coupon rate of $10\%$ paid annually, $3$ years to maturity, a par value of $$1,000,$ and the yield to maturity of $8\%\mathrm{.}1)$ Figure out the duration of the bond. $(40$points$)$For duration i$)$ Macaulay duration ii$)$ Modified duration Present value of each coupon, PV $=$ Coupon rate $/(1+$yield$)^$n$2)$ You believe that the Fed is about to decrease interest rates by $30$ basis points $(0\mathrm{.}3\%).$ Figure out the percentage change in the bond price and the direction $($increase$/$decrease$)$ of the price change using the duration. $($If you cannot figure out the duration, use a duration of $3.)(30$points$)$