A pension company has an investment portfolio that consists of three types of bonds: (i) Twenty-year bond with annual coupon of 4%, (ii) Thirty-year zero coupon bond, (iii) A perpetuity immediate making annual payments. You are given that the interest rate is 3%. Find the fraction of the portfolio invested in the twenty-year bond if you are given that the duration of the entire portfolio is 18, while the duration of the portion of the portfolio excluding the twenty-year bond is 21.