A mortgage calculator is one formula, a loop, and a rounding decision. The formula is the easy part. The rounding decision is the one your users will actually notice.

I built a mortgage calculator as a static page — no backend, everything in the browser. The core question it answers sounds trivial: given a loan amount, a rate, and a term, what fixed monthly payment brings the balance to exactly zero? The formula is closed-form, the code fits in under 40 lines, and yet the first version I shipped disagreed with every bank statement I tested it against — by cents. Cents, it turns out, are where calculator credibility lives.

The one formula

The payment that amortizes a loan is the present value of an annuity, solved for the payment:

M = P × r(1 + r)ⁿ / ((1 + r)ⁿ − 1)

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P is the loan amount, r is the monthly rate (annual ÷ 12), n is the number of payments.…