Yes. Your lender requires comprehensive and collision coverage independently of anything the state requires. The certificate speaks only to liability, so the policy has to satisfy two different requirements at once.
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This is the reality for most drivers in the newer growth suburbs, Papillion and the west side of the metro especially, where a high share of vehicles carry a loan. The temptation under a post-violation premium is to drop physical damage coverage to get the payment down. That satisfies the state and breaches the loan agreement. Lenders respond by force-placing coverage, which is expensive, protects the lender rather than the driver, and gets added to the loan balance. It is close to the worst financial outcome available in this situation. If the premium is genuinely unaffordable, the better conversations are about deductibles, payment plans, and shopping several nonstandard carriers, all of which keep the loan agreement intact.