Consider a sequential pay CMO that is backed by 125 mortgages with average balance of $100,000 each. The mortgages have monthly payments with WAM = 15 years and WAC =7%. There is a servicing fee of 0.3% and prepayment is according to 200% PSA. Tranche A holds $7,000,000 of the mortgage pool principal at origination, tranche B holds $3,000,000 and tranche Z holds $2,000,000. The rest of the pool principal is held by the SPV as a residual. The SPV has set a pass-through rate (coupon rate net of the servicer/guarantee fee) of 5.5% for Tranche A, 5.75% for Tranche B and 6.5% for Tranche Z. At the beginning of month 7, the overall mortgage pool balance has 12,173,352.58 of principal remaining. Of that overall principal at the beginning of month 7, Tranche A holds 6,607,465.99, Tranche B holds 3,000,000 and Tranche Z holds 2,065,886.59. What is tranche A's outstanding principal balance at the end of month 7 (beginning of month 8)?

[Note: You can answer this question starting with the fact that "At the beginning of month 7, the overall mortgage pool balance has 12,173,352.58 of principal remaining" without deriving cash flows for all periods before and after]