None of the $16,000 interest paid by Carol on the equity debt ($350,000) used to purchase a vacation home is deductible since it doesn't qualify for the deduction.
Under the tax laws in the United States, interest paid on equity debt used for purposes other than improving the primary residence or acquiring it is not deductible. In this case, since Carol used $350,000 of equity debt from her primary residence to purchase a vacation home, the interest on the debt related to the vacation home is not deductible.
Therefore, Carol cannot deduct any portion of the $16,000 interest paid on the debt for the vacation home. It's important to note that tax laws are subject to change, and individual circumstances may vary, so it's advisable to consult with a tax professional for specific and up-to-date advice.