Sarah is considering two different car insurance plans. Plan A has an annual premium of $1,200 and covers 70% of any accident repairs. Plan B has an annual premium of $900 and covers 50% of any accident repairs. Sarah estimates that she might need about $2,000 worth of repairs per year. Considering the annual premium and the estimated repair costs, which plan is more cost-effective for Sarah, and by how much? Let's think step by step and output the final answer within \boxed{}.
user