You are a bond portfolio manager who is in the business of providing a guaranteed rate of return to your clients over a given investment horizon. The following information has been provided to you on bonds X and Y

Bond Coupon Maturity Price

X 8% 10 Years 96.72

Y 9% 30 Years 105.37

1. What fractions should be invested in X and Y to obtain a portfolio with duration of a) 8 years b) 9 years c) 10 years?