No borrower has ever repaid a rate. They repay a schedule: a list of dates and a list of amounts. The rate is an input. The schedule is the product, and it is the only part of the definition the borrower will ever see.
An installment product is a promise about arithmetic. A fixed sum, drawn once, repaid over equal periodic payments, each one splitting into interest and principal in a proportion that moves every period. Early payments are mostly interest. Late payments are mostly principal. The borrower pays the same amount every month and the composition underneath it changes silently.
# Principal Interest Payment 01 724.90 680.00 1,404.90 02 765.98 638.92 1,404.90 03 809.37 595.53 1,404.90 04 855.19 549.71 1,404.90 … 12 1,325.35 79.55 1,404.90
The rounding rule is part of the definition
Twelve equal payments rarely divide a loan cleanly. Somewhere a fraction of a centavo has to go, and where it goes is a decision. The engine keeps money in integer minor units and rates in basis points, computes the payment exactly, and applies one rounding step defined by the market rule (half-even, two decimal places). The residue lands in the final installment, which is why the last row is never quite a twin of the first eleven.
This is not a detail an operations team should discover on a live book. A product whose schedule can be reproduced two ways is a product with two answers to a borrower dispute.
A product is a surface, not a loan
A definition that allows MXN 5,000 to 60,000 over 6 to 24 months does not describe one schedule. It describes every schedule inside that range. The cost is not constant across it: fixed and up-front charges weigh heaviest on the smallest, shortest loan, so the annual cost peaks in the corner nobody prices by hand.
That corner is where a product breaks. It is where the CAT approaches the legal cap, and it is where an origination fee can grow so large that the smallest allowed loan cannot cover its own first payment. Simulation runs the corners, not the happy path.
Signed once, replayed forever
The schedule a manager approves is the schedule the loan runs on. The product version is frozen and signed, every loan binds to the exact version it originated under, and the ledger appends what the schedule said should happen and what actually did. Two years later, the question is not what the terms probably were. It is a replay: same version, same rules, same twelve rows.