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The Other Dependent Credit is not a "refundable" credit, meaning that the credit can’t be used to increase your tax refund or to create a tax refund when you wouldn’t have already had one.  Therefore, if your tax due was less than $500, the credit can only reduce your tax due to $0.  Here is an example: 

The credit savings cannot exceed the amount of tax you owe. For example, if the only credit you’re eligible for is a $500 Child and Dependent Care Expenses credit, and the tax you owe is only $200—the $300 excess is nonrefundable. This means that the credit will eliminate the entire $200 of tax, but you don’t receive a tax refund for the remaining $300.

From:   TurboTax Article:  What is the Difference Between a Refundable and Non-Refundable Credit?

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