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)?

Please explain each step.