Is there an explanation for these mortgage results?

I just used a mortgage calculator provided online by a real estate firm in the Midwest to come up with the following for three different (theoretical) down payment amounts

Price (In the neighborhood of ) $ 489,000
Down Payment $ 400/4000/40,000
Interest Rate 4%
Mortgage Term 30 years
Payment $ 2, 338 / 2, 320 / 2, 137

This may not be all banks’ takes, and the interest rate may affect things a little, but isn’t mortgage rate suppose to be somewhat uniform across the board in the US? As it stands, there seems precious little monthly advantage to making a larger down payment. Why is that? Why is it that so much is required.

The mortgage calculator at (for example) doesn’t even take into account your initial down payment, only the loan amount. Is that an important difference?

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