Do individuals prefer a fixed-price multi-year insurance (MYI) policy to current annual contracts with fluctuating prices? If so, are they willing to pay more for these policies? In a web-based 2-period repeated game with significant real money at stake, individuals have an opportunity to purchase 1-period insurance contracts, 2-period contracts or no insurance against the risk of a hurricane causing damage to their property. When premiums for both insurance options are actuarially fair, more than five times as many people favor the 2-period contract over the 1-period contract. The demand for a 2-period contract remains high even with a loading cost of 5% and 10% while keeping the 1-period premium actuarially fair, indicating a preference for stable premiums over time. These findings support the need for multi-year contracts that will lead more individuals to be adequately protected against future extreme events, given the empirical evidence on lack of interest in insurance against catastrophic risks.