How should they architect their solution?

Explanations:

This option uses NAT instances to allow the application instances to communicate with the payment service while keeping their private IPs secure. The Elastic IPs of the NAT instances can be whitelisted, ensuring that all outgoing traffic from the application instances uses these static IP addresses. This setup also supports high availability by deploying two NAT instances.

Whitelisting the VPC Internet Gateway Public IP is not valid because the Internet Gateway does not have a fixed public IP. Instead, it allows communication between the VPC and the Internet but does not assign a static IP that can be whitelisted. Additionally, routing traffic directly through the Internet Gateway does not provide a controlled way to manage the limited number of whitelisted IPs.

Whitelisting the ELB IP addresses is not a viable solution because the ELB IP addresses can change. ELB uses a pool of IP addresses that can vary over time, which makes it unreliable for whitelisting in this context. Moreover, traffic routed through the ELB does not guarantee that the same IP will be used for outbound connections.

This option would involve dynamically assigning public IPs to EC2 instances, which could lead to more than four IPs being active at peak times due to the scaling of the Auto Scaling group. The solution requires maintaining a maximum of four whitelisted IPs, which this method does not guarantee, making it impractical for the requirement of whitelisting a limited number of IP addresses.