The duration of 10-year maturity bonds with coupon rates of 6% (paid annually) is eight years and the duration of 6-year maturity bonds with coupon rates of 12% (paid annually) is five years. Kathryn manages a pension fund that will provide retired workers with lifetime annuities. She determines that the payouts of the fund are going to closely resemble level perpetuities of $1.3 million per year. The interest rate is 17%. Kathryn plans to fully fund the obligation using a 6-year and a 10-year maturity coupon bonds.

(a) Find the duration of the funds payouts.

(b) If Kathryn wants to fully fund and immunize her payouts, what are the proportions (in $) of the investment that she should invest in the bonds?