According to the Florida Department of Financial services, you cannot cancel your FL auto insurance policy during the first 60 days unless you can provide proof of one of the following: the vehicle is totally destroyed, you sold the vehicle or you obtained coverage with another company.

You may cancel your automobile insurance policy at any time following the first 60 days after its effective date by notifying your insurance company in writing. If you do so, the insurance company may charge you a 10 percent penalty on your returned premium.

Since you have already started a policy and have had use of it on your vehicle for a week with your current insurance company it would be doubtful that you could receive a full refund.

If you have obtained insurance with the cheaper insurance company, you will need to inform the first company, request cancellation and a refund. They should be able to tell you how much of a refund you should receive.

It is important to comparison shop for insurance of any type before purchasing a policy. The rating systems for insurance premiums vary from company to company so the price of insurance will also differ. Why Should You Show Around for Auto Insurance? is an article in our learning center than you might find helpful at this time.