A company will operate stateful web applications on EC2 instances in an Auto Scaling group, running continuously all year. The business wants the flexibility to change instance sizes within the same instance family later in the year based on usage patterns. Which EC2 purchase option offers the most cost-effective solution while meeting this requirement?

Convertible Reserved Instances are the most cost-effective solution because they offer significant discounts (up to 54% compared to On-Demand) and provide the flexibility to exchange them for other Convertible RIs with different instance families, operating systems, or tenancies. This meets the requirement of changing instance sizes within the same family later. On-Demand Instances are flexible but significantly more expensive. Spot Instances are the cheapest but are unsuitable for continuously running, stateful applications due to their interruptible nature. Standard Reserved Instances offer higher discounts than Convertible RIs but lack the flexibility to change instance families, making them unsuitable for the stated requirement.