Denny was neither bankrupt nor insolvent but was short of cash and could not make the mortgage payments on his personal residence in 2011. The bank that held the mortgage agreed to reduce the principal on the debt from $100,000 to $80,000 so that Denny's monthly mortgage payments could be reduced to a manageable amount. Denny also had a vacation home with a mortgage whose payments were beyond his means. The mortgage holder on the vacation home agreed to reduce the mortgage from $60,000 to $50,000. The value of the personal residence was $80,000 and the value of the vacation home was $45,000 at the dates of the debt reduction

Which of the following is correct?:

Denny is not required to recognize any income as a result of the reduction in the principal of the mortgages. Denny is required to recognize $5,000 income from the reduction in the mortgage on the vacation home, but has no gross income from the reduction in the mortgage principal on his personal residence. Denny is required to recognize $10,000 income from the reduction in the mortgage on the vacation home, but nothing for the reduction in the mortgage on his personal residence. Denny is required to recognize $10,000 income from the reduction in the mortgage on the vacation home and $20,000 income for the reduction in the mortgage on his personal residence. None of the above