5. A bank has two, 3-year commercial loans with a present value of $70 million. The first is a $30 million loan that requires a single payment of $37.8 million in 3 years, with no other payments until then. The second is for $40 million. It requires an annual interest payment of $3.6 million. The principal of $40 million is due in 3 years. Suppose the interest rate is 8%.

a. What is the Macaulay duration of the first loan?

b. What is the Macaulay duration of the second loan?

c. What is the Macaulay duration of the banks commercial loan portfolio?