How can insurance companies afford to pay for an individual's catastrophic loss?

The correct choice highlights the fundamental principle of insurance known as risk pooling. Insurance companies rely on the concept that not all policyholders will suffer a catastrophic loss at the same time. When individuals purchase insurance, they pay premiums, which are then pooled together by the insurer. This collective pool of funds is used to cover the losses of those few who do experience significant claims.

By spreading the risk across a large number of policyholders, insurance companies can predict and manage their potential liabilities more effectively. This allows them to assure individual policyholders that they will be covered for major losses, despite the fact that the payouts for these events can be substantial.

Considering the other provided options, they do not correctly explain how insurance companies effectively manage risk and fund payouts for catastrophic losses. For instance, simply placing premium payments into an interest-bearing account does not address the collective nature of insurance risk. Limiting payments to amounts previously collected from policyholders overlooks the pooling mechanism, as it suggests an individual basis of insurance rather than the collective support system in place. Lastly, denying claims due to insufficient funds would undermine the very purpose of insurance and lead to a lack of trust and security for the policyholders.