Please show all work and explain. Answere are given.

Consider a six$-$year, $6\mathrm{.}5\%$ coupon bond and an eight$-$year, $7\mathrm{.}25\%$ coupon bond. Without making any

calculations, what can you determine about the two bonds$$ relative durations? Explain.

$28.$ Take the two bonds from question #$27$ and assume that the YTM for both bonds is $5\mathrm{.}5\%.$ Compute

their prices. If the YTM on the first bond goes up to $6\mathrm{.}5\%$ and the YTM on the second goes up to

$7\%,$ what will be the change in each bond$$s price? $$1,049\mathrm{.}96$; $$1,110\mathrm{.}85$; $-4\mathrm{.}76\%$; $-8\mathrm{.}63\%$

$29.$ Consider a $12-$year $5\mathrm{.}5\%$ coupon bond and a nine$-$year $7\mathrm{.}5\%$ coupon bond. Without making any

calculations, which bond do you believe is more sensitive to interest rate changes? Explain.

$30.$ Take the two bonds from question #$29$ and assume that the YTM for both bonds is $7\mathrm{.}0\%.$ Compute

their prices. If the YTMs on the two bonds decline to $6\mathrm{.}0\%,$ what will be the percentage change in

each bond$$s price? $$880\mathrm{.}86$; $$1,032\mathrm{.}58$; $8\mathrm{.}77\%$; $6\mathrm{.}73\%$