7. (15 points) Cash flow 1 consists of three payments: A is 5 periods, B in 10 periods and C in 15 periods. Cash flow 2 consists of 2 payments: X in 6 periods and Y in 12 periods. As of now, at yield j per period for all maturities, the two sets of cashflows have the same present value and the same Macaulay duration. Suppose that one period from now the yield is still j for all maturities. Show that (a) (5 points) the two sets of cash flows will have the same present value at t=1); (b) (5 points) the two sets of cash flows have the same Macaulay duration at that time; and (e) (5 points) the Macaulay duration one period from now is exactly 1 less than it is now. 7. (15 points) Cash flow 1 consists of three payments: A is 5 periods, B in 10 periods and C in 15 periods. Cash flow 2 consists of 2 payments: X in 6 periods and Y in 12 periods. As of now, at yield j per period for all maturities, the two sets of cashflows have the same present value and the same Macaulay duration. Suppose that one period from now the yield is still j for all maturities. Show that (a) (5 points) the two sets of cash flows will have the same present value at t=1); (b) (5 points) the two sets of cash flows have the same Macaulay duration at that time; and (e) (5 points) the Macaulay duration one period from now is exactly 1 less than it is now