The prices of zero-coupon bonds with various maturities are given in the following table. Suppose that you want to construct a 2-year maturity forward loan commencing in 3 years. The face value of each bond is $1,000. a. Suppose that you buy today one 3-year maturity zero-coupon bond with face value $1,000. How many 5-year maturity zeros would you have to sell to make your initial cash flow equal to zero (specifically, what must be the total face value of those 5-year zeros)? b. What are the cash flows on this strategy in each year? c. What is the effective 2 -year interest rate on the effective 3-year-ahead forward loan? d. Confirm that the effective 2-year forward interest rate equals (1+f4)(1+f5)1. You therefore can interpret the 2-year loan rate as a 2-year forward rate for the last two years. Alternatively, show that the effective 2-year forward rate equals (1+y3)3(1+y5)51