Work out late-payment interest and compensation from part payments, credit notes and a base-rate change

# Work out a design studio's late-payment interest and compensation Inputs: `invoices.csv` (inv_id, client, issued, due, amount), `credits.csv` (inv_id, amount), `payments.csv` (payment_id, client, paid_on, amount), `base-rates.csv` (from_date, rate), `terms.json` and `bookkeeper-note.txt`. Amounts are in pounds. `terms.json` and these rules are the record; where the bookkeeper's note disagrees, the rules win. Rules: - Clients match ignoring letter case and surrounding spaces; report them in upper case. A credit note reduces its invoice's amount from the start. - Payments are applied in paid_on order (ties by payment_id), each to the client's invoices with the earliest due date first (ties by the invoice number), filling one before the next; anything left over is unapplied. - Interest accrues for each day after the due date up to and including as_of on the amount still unpaid at the end of that day, at (statutory_pct + the base rate in force on that day) percent a year, divided by 365; each invoice's interest is rounded half-up to 0.01 once, at the end. - An invoice still unpaid at as_of, or paid in full only after its due date, earns one compensation fee from the first terms.json band whose `below` is more than its amount after credit notes (`below` null is the top band); an invoice paid in full on or before its due date earns none. - Write `out/late-payment.json`: `{"balances": {"<inv_id>": <unpaid at as_of>, ...}, "unapplied": {"<CLIENT>": <amount>, ...}, "interest": {"<inv_id>": <interest>, ...}, "compensation": {"<inv_id>": <fee>, ...}, "client_totals": {"<CLIENT>": <balances + interest + compensation>, ...}}`. `balances` and `client_totals` cover every invoice and client; the other maps list only amounts above 0. ## How this run works - Work on your own: nobody will answer questions in this task, and writing to `ask/` counts against the run. - Write only under `out/`. Create `out/` if it is missing. Inputs are synthetic; don't fetch anything from the network. - Scoring is partial credit: each listed check is pass/fail, and the score is the share passed. Numbers are compared to within 0.005 unless the task says otherwise.