Question $1.(11$ points$)$

a$.$ Find the duration of a $8\%$ coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of $12\%.$

b$.$ If you wants to fully fund and immunize its position, how much of your

portfolio should allocate to two year zero$-$coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan?

c$.$ How will these fractions change next year if your $8\%$ coupon bond

duration also drop one year?