An insurance company is obligated to make a payment of $200,000 in 5 years. Its managers plan to fund this liability by purchasing a one-year zero-coupon bond, a two-year zero- coupon bond, and a six-year zero-coupon bond, all purchased today. The current yield rate for all bonds is 3%, and the managers plan to invest (today) $X, $X in the first two bonds, and $Y in the

third. (That is, for example, the two-year zero-coupon bond will return 1.032 $X in 2 years.)

Compute the values of X and Y so that the first two of Redington immunization conditions are achieved.