Suppose you purchase a $30-$year, zero$-$coupon bond with a yield to maturity of

$6\mathrm{.}4\%.$ You hold the bond for five years before selling it$.$

a$.$ If the bond's yield to maturity is $6\mathrm{.}4\%$ when you sell it$,$ what is the annualized

rate of return of your investment?

b$.$ If the bond's yield to maturity is $7\mathrm{.}4\%$ when you sell it$,$ what is the annualized

rate of return of your investment?

c$.$ If the bond's yield to maturity is $5\mathrm{.}4\%$ when you sell it$,$ what is the annualized

rate of return of your investment?

d$.$ Even if a bond has no chance of default, is your investment risk free if you

plan to sell it before it matures? Explain.