Assume there are a bunch of mortgages that are supposed to pay principal payments and interest payments of $2100 during the year are pooled together and sold as securities. These securities have tranches which include I, II, III, and IV. Tranche I is supposed to collect $1000 in principal, tranche II is supposed to collect $500 in principal, tranche III is supposed to collect $300 in principal, and Tranche IV is supposed to collect $200 in principal. Tranche IV has the highest yield assuming that all principal is paid. The annual total interest cost is $100, and this is paid before principal is paid to any of the tranches.
Assume that homeowners default on their mortgages and they only pay $1200 during the year. How much does tranche II collect in principal?