A financial institution has to pay $1,000 after 2 years and $2,000 after 4 years. The current market interest rate is 10%, and the yield curve is assumed to be flat at any time. The institution wishes to immunize the interest rate risk by purchasing zero-coupon bonds which mature after 1, 3 and 5 years. One member in the risk management team of the institution, Sam, devised the following strategy Purchase a 1-year zero-coupon bond with a face value of $454.55 Purchase a 3-year zero-coupon bond with a face value of $1,459.09 Purchase a 5-year zero-coupon bond with a face value of $1,100.00 Show that Sam's portfolio satisfies the conditions of the full immunization strategy