Problem 3. A company owes several debts in the upcoming years: $300 at time 2, and $200 at time 5. The company plans to meet the obligations with investments in three zero-coupon bonds, each paying off at time 1, 3, and 4. Knowing that the 3-year zero coupon bond is paying off $100, how much payoff should the company purchase from the other two bonds such that the balance sheet is duration-wise matched? Does the suggested portfolio pass the convexity check? (Evaluate at an effective interest rate of 10%, assume bonds allow purchase of any payoff) Problem 3. A company owes several debts in the upcoming years: $300 at time 2, and $200 at time 5. The company plans to meet the obligations with investments in three zero-coupon bonds, each paying off at time 1, 3, and 4. Knowing that the 3-year zero coupon bond is paying off $100, how much payoff should the company purchase from the other two bonds such that the balance sheet is duration-wise matched? Does the suggested portfolio pass the convexity check? (Evaluate at an effective interest rate of 10%, assume bonds allow purchase of any payoff)