$3\mathrm{.}1$ Sally Zide is considering the purchase of one of the two bonds. She realises her decision will depend primarily on effective duration, and she believes that interest rates will decline by $25$ basis points at all maturities over the next $6$ months. The characteristics of the two bonds under consideration are the following: Characteristic Bond One Bond Two Market price $101\mathrm{.}25101\mathrm{.}25$ Maturity date $1$ June $20221$ June $2022$ Call date Non$-$callable $1$ June $2017$ Annual coupon $5\mathrm{.}5\%6\mathrm{.}55\%$ Interest payment Semi$-$annual Semi$-$annual Effective duration $7\mathrm{.}255\mathrm{.}30$ Yield to maturity $5\mathrm{.}02\%6\mathrm{.}10\%$ Credit rating A A$3\mathrm{.}1\mathrm{.}1$ Calculate the percentage change. Show the relevant equation. $(5)3\mathrm{.}1\mathrm{.}2$ Calculate the $6-$month horizon return in percentage for each bond, if the actual Bond One bond price equals $105\mathrm{.}75$ and the actual Bond Two price equals $104\mathrm{.}35$ at the end of the $6$ months. Show the relevant equation. $(5)3\mathrm{.}2$ You have purchased a bond for R$973\mathrm{.}02.$ The bond has a coupon rate of $6\mathrm{.}4\%,$ pays interest annually, has a face value of R$1000,4$ years to maturity, and a yield to maturity of $7\mathrm{.}2\%.$ The bond's duration is $3\mathrm{.}6481$ years. You expect that interest rates will fall by $0\mathrm{.}3\%$ later today. Use the modified duration to find the approximate percentage change in the bond's price.