Debt 1: mortgage math that ties

A fixed-rate amortizing loan has one payment solving PMT = P·r ÷ (1 − (1+r)^−n), with r the monthly rate and n the total months. Each payment splits into interest (balance × r) and principal (the rest); balances therefore fall slowly early and quickly late. A $13.5M loan at 4.35% over 25 years pays ≈ $73,893 monthly; the same loan over 30 years pays ≈ $67,205 — lower payment, slower equity build, more total interest.

Vocabulary: amortization (the schedule length) vs term/maturity (when the balance is due — often shorter, creating a balloon). Interest-only periods hold the balance flat. The loan constant (annual debt service ÷ original principal) lets you compare financings in one number.

Discipline: any quoted payment or balance should re-derive from rate, amortization and elapsed payments — to the dollar. Numbers that do not tie are how spreadsheets acquire legends.