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Part $1$

Suppose you purchase a$30-$year, zero$-$coupon bond with a yield to maturity of $9\%.$ You hold the bond for five years before selling it$.$

a$.$ If the$$ bond's yield to maturity is $9\%$ when you sell$$ it$,$ what is the internal rate of return of your$$ investment?

b$.$ If the$$ bond's yield to maturity is $10\%$ when you sell$$ it$,$ what is the internal rate of return of your$$ investment?

c$.$ If the$$ bond's yield to maturity is $8\%$ when you sell$$ it$,$ what is the internal 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.