IV$.$ Duration, yield to maturity, and the expectation hypothesis What is the duration of a $4-$year bond with an annual coupon of $22\mathrm{.}0\%$ and a $29\mathrm{.}0\%$ yield to maturity: $($a$)3\mathrm{.}36$; $($b$)2\mathrm{.}96$; $($c$)4\mathrm{.}00$;$($d$)3\mathrm{.}76$; What is the present discounted value of the final coupon and face value of this bond: $($a$)84\mathrm{.}58$; $($b$)92\mathrm{.}22$; $($c$)94\mathrm{.}99$; $($d$)44\mathrm{.}06.$ What is the duration of a $3-$year bond that pays annual coupons of $3\%$ only in years $2$ and $3$ with a yield to maturity of $15\%$ : $($a$)2\mathrm{.}97$ ;$($b$)1\mathrm{.}98$ ;$($c$)2\mathrm{.}83$ ; $($d$)$ duration cannot be computed for a bond that does not pay a coupon every period; What is the approximate linear yield to maturity on a $6-$year bond with a face value of $$100$ and a $12\%$ annual coupon selling at $$102$ : $($a$)11\mathrm{.}55\%$; $($b$)10\mathrm{.}90\%$; $($c$)13\mathrm{.}68\%$; $($d$)12\mathrm{.}00\%$; Assume that current one$-$year Treasury yields r$\_(1,$t$)=5\%$ and current two$-$year yields r$\_(2,$t$)=9\%.$ What liquidity premium for a two$-$year bond would make expected one year yields r$\_(1,$t$+1)^($e$)$ equal to current one$-$year yields: $($a$)400$ basis points; $($b$)4\mathrm{.}30\%$; $($c$)1\mathrm{.}5\%$; $($d$)-4\mathrm{.}00\%$;