$400 million pass-through MBS, 'seasoning' of the pass-through is equal

Given : $400 million pass-through MBS, 'seasoning' of the pass-through is equal to 0, maturity of 20 years and an annual mortgage coupon rate of 6%, The pass-through rate of the mortgage pool is 5%. prepayment multiplier of 100 PSA

Q1:Suppose we construct principal-only (PO) and interest-only (IO) mortgage-backed securities (MBS) using the mortgage pass-through of the previous questions. Assume a prepayment multiplier of 100 PSA. What is the present value of the PO MBS if we use an annual risk-free rate of 4.5% to value the cash-flows?

Q2:Referring to the previous question, what is the value of the IO MBS?

Q3:Referring to the previous question, what is the average life of the IO MBS?

Q4:Suppose now that you purchased the IO MBS of the previous question and that the price you paid was the same price that you calculated in the previous question. The risk-free interest rate suddenly changes from 4.5% to 3.5%. Everything else stays the same. How much money have you made or lost on your investment?

Q5:

Referring to the previous question, suppose the risk-free interest rate suddenly changes from 4.5% to 3.5% and that the pre-payment multiplier changes from 100 PSA to 150 PSA. How much money have you made or lost on your investment in the IO MBS?