Suppose a x% annually paid bond has a maturity of 10 years. The redemption value, which equals to its face value, is $100. The issuer has the option to redeem the bond at t = 7, t = 8, t = 9 or t = 10.

(a) Find the lowest possible yield rate if the price is $90.

(b) Find the lowest possible price if the yield rate is 6.5%.