A company wants to issue a 20-year $1000 bond with semi-annual coupons at a nominal annual coupon rate of 5%. The bond is callable at the end of x years, y years, and 20 years with a redemption amount of $1100. You are given the following requirements:

1. The company wants to offer an annual effective yield rate no more than i = 5.5%.
2. The price P of the bond should satisfy $920 P $1080.
3. There are at least 5 years between any two callable dates.

a. List all possible pair values of (x, y) satisfying the above three requirements.

b. For each pair, write down an equation satisfied by the highest semi-annual effective yield rate that a bondholder can earn.