We consider the following zero$-$coupon curve:

Maturity $($Years$)$ Zero$-$ Coupon Rate $\%$

$14\mathrm{.}0$

$24\mathrm{.}5$

$34\mathrm{.}75$

$44\mathrm{.}90$

$55\mathrm{.}0$

$1.$ What is the price of a $5-$year bond with a $$100$ face value, which delivers a $5\%$ annual coupon rate?

$2.$ What is the yield to maturity of this bond?

$3.$ We suppose that the zero$-$coupon curve increases instantaneously and uniformly by $0\mathrm{.}5\%.$ What is the new price and the new yield to maturity of the bond? What

is the impact of this rate increase for the bondholder?

$4.$ We suppose now that the zero$-$coupon curve remains stable over time. You hold the bond until maturity. What is the annual return rate of your investment? Why

is this rate different from the yield to maturity?