Suppose you purchase a $30-$year, $$zero$-$coupon bond with a yield to maturity of $6\mathrm{.}2\%.$ You hold the bond for five years before selling it$.$

a$.$ If the$$ bond's yield to maturity is $6\mathrm{.}2\%$ when you sell$$ it$,$ what is the annualized rate of return of your$$ investment?

b$.$ If the$$ bond's yield to maturity is $7\mathrm{.}2\%$ when you sell$$ it$,$ what is the annualized rate of return of your$$ investment?

c$.$ If the$$ bond's yield to maturity is $5\mathrm{.}2\%$ when you sell$$ 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.