(5) A company has to pay 4000 at the end of year 4, 6000 at the end of year 10, and 400 at the end of year 12. If the effective annual rate is 5%, find the modified duration of these payments. (6) A company has liabilities of 3000 and 5000 due at the end of years 3 and 5 respectively. The company can invest in the following bonds: . A 5-year 1000-par bond that pays annual coupons at a rate of 5%. A 3-year 1000-par bond that pays annual coupons at a rate of 3%. If both bonds has a yield of 2%, find how much the company should invest in each bond to match the liabilities (You must match the present values and the duration).