Suppose that you are tasked with managing a liability of $5,000 worth of 6% 4-year, annual coupon bonds when the interest rate is 4.5%. You want to minimize the interest rate risk by immunizing this position through value and duration matching. If you have 2-year and 10-year zero-coupon bonds available to create the hedge, how many dollars should you invest in each bond? Explain at least three reasons this hedge will not be perfect one year after you set it up.