Undertow
Public market-depth and sized exit estimates, not executable quotes

Mortgage payment, amortization, affordability and 50-state property tax data.
US Mortgage Calculator API is a free Finance API that requires no API key, is served over HTTPS and supports CORS, so it can be called from the browser.
Free mortgage calculation REST API. Eleven JSON endpoints covering payments, amortization, affordability, refinance, closing costs and 50-state property tax data. No key required.
Details from usmortgagecalc.com.

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Public market-depth and sized exit estimates, not executable quotes
The US Mortgage Calculator API is provided by US Mortgage Calculator (usmortgagecalc.com). Free mortgage calculation REST API. Eleven JSON endpoints covering payments, amortization, affordability, refinance, closing costs and 50-state property tax data. No key required.
Yes. The US Mortgage Calculator API is listed in the Finance category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
No. The US Mortgage Calculator API requires no authentication, so you can start making requests without signing up.
Yes. The US Mortgage Calculator API supports CORS, so front-end JavaScript can call it directly.
Yes. The US Mortgage Calculator API is served over HTTPS, so it's safe to use in production.