Not Using Excel $-$ Question $1$ A bond has a par value of $$100,$ a time to maturity of $2$ years, and a coupon rate of $10\%$ with interest paid annually.

a$.$ The yield to maturity of the bond is $5\%.$ What is the price of this bond?

b$.$ Suppose the yield curve is given by the following table

$1$y $2$y $4\%?$

The yield to maturity of a $1-$year zero$-$coupon bond is $4\%.$ Suppose no arbitrage opportunities exist. What is the yield of a $2-$year zero$-$coupon bond?

c$.$ Find the modified duration of this bond. Suppose the yield increased by $5\%,$ what

is your estimate of the percentage change in the bond$$s price using modified duration?

d$.$ Find the convexity of this bond. What is your estimate of the percentage changein the bond$$s price using both modified duration and convexity?