The most cost-effective and fault-tolerant solution for managing EC2 instances with predictable peak traffic is to use an Auto Scaling group (Option A). This feature automatically scales the number of EC2 instances up or down based on the demand, ensuring that the company has the necessary resources during peak times and can save costs by reducing the number of instances during off-peak times. Purchasing Reserved Instances (Option B) would provide constant peak capacity but is not cost-effective as it requires paying for capacity that is not always needed. Stopping EC2 instances during low demand (Option C) could save costs but does not ensure the availability and fault tolerance required. Vertically scaling EC2 instances (Option D) requires continuous management and is not cost-effective as it may involve purchasing more resources than necessary.