If you're not already living on a written, monthly budget, that should be the first step. You say your parents don't need the money, right? So, they're not living on bread and water without your payments. I think the biggest thing causing them stress is the fear that you're being irresponsible.
Make out a simple, realistic budget, and sit down with them to explain what you're doing and how you plan to address things. Start a debt snowball, and begin knocking out your debts smallest to largest. By the time you pay off the credit cards and the car, you'll be able to give them lots more than $200 a month.
Just ask Mom and Dad to stick with you a while longer. I think it will make them feel better to see that you're serious about getting your finances in order.
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