Multi-currency ledger

Design a multi-currency ledger for a cross-border money app where a user holds balances in 30+ currencies and can convert between them at a quoted rate. ~6,000 conversions/sec. Each conversion debits one currency balance and credits another at a locked FX rate, and the company books a spread as revenue. Describe the data model, how you avoid rounding/precision errors that leak or create money, and how you keep per-currency balances correct and reconcilable.