IV$.$ Duration, yield to maturity, and the expectation hypothesis

$19.$ What is the yield to maturity on a $6-$year bond with a face value of $$100$ and a $4$:$5\%$ annual coupon selling at $$103$:$00$: $($a$)6\mathrm{.}00\%$; $($b$)4\mathrm{.}48\%$; $($c$)3\mathrm{.}94\%$; $($d$)5\mathrm{.}80\%$;

$20.$ If a $2-$year bond is yielding $6$:$25\%$ and selling at par, what is the $1-$year rate next year if the bond price falls to $$99$:$00$: $($a$)6\mathrm{.}25\%$; $($b$)7\mathrm{.}25\%$; $($c$)4\mathrm{.}28\%$; $($d$)2\mathrm{.}00\%$;

Consider a $3-$year bond with a face value of $$100,$ a $3\%$ yield to maturity, and a $12\%$ annual coupon.

$21.$ What is the duration: $($a$)2\mathrm{.}72$; $($b$)3\mathrm{.}91$; $($c$)12$; $($d$)3\mathrm{.}00$;

$22.$ By how much would the bond price rise if the yield to maturity fell to $2\%$: $($a$)3\%$; $($b$)12\%$; $($c$)3\mathrm{.}68\%$; $($d$)2\mathrm{.}64\%$;

$23.$ A $2-$year bond with a yield to maturity of $2$:$75\%$ has a duration of $1$:$87.$ What is the annual coupon: $($a$)17\%$; $($b$)2\mathrm{.}50\%$; $($c$)1\mathrm{.}87\%$; $($d$)13\%$;

$24.$ A bond has a price of $$103$:$75,$ a coupon of $2$:$50\%,$ and a yield to maturity of $2$:$166\%.$ How many years till the bond matures: $($a$)7$; $($b$)24$; $($c$)13$; $($d$)19$;