Assume that after buying insurance, drivers can choose to drive safely or drive recklessly. Driving safely or recklessly, each come with their own benefits and costs for the driver, so they each have a different net benefot for the driver. Assume that driving safely brings a net benefit to the driver of $$200,$ while driving recklessly brings a net benefit to the driver of $$500.$ Also, depending on driving habits and also on luck, the driver will avoid or be engaged in accidents. If the driver drives safely and he is also lucky, he avoids getting into an accident. If he drives recklessly and he is lucky, he will experience a minor accident. The driver will also experience a minor accident if he drives safely but he is unlucky. Finally, if the driver drives recklessly and he is also unlucky, he will get involved in a major accident. Assume a minor accident costs the insurance company $500,$ while a major accident costs them $3000.$ Assume also that the driver is lucky with probability $0\mathrm{.}78.$ The insurance company is designing an insurance contract to try to correct moral hazard problems and incentivize the drivers to drive safely by introducing a deductible in the contract. A deductible is a sum of money that has to come up from the driver's pocket in case of an accident, before the insurance company pays anything. So a deductible acts as a cost to the driver, if he has an accident $($regardless if it's a minor or major accident$).$ What should be the minimum deductible charged by the insurance company, to incentivize the driver to drive safely? Round your answer to $2$ decimals, if needed.