How does a down payment affect a mortgage?

I am a first time home buyer looking to get a mortgage for a house. My question is how I can include the down payment into the mortgage calculations. Let’s say that the sale price is $ 200,000 and we are able to put 20% down ($ 40k). This will be at 3.5% for 30 years with monthly payments.

My question is, will the mortgage amount be for $ 200,000? Or will it be for $ 160,000 after we subtract the down payment?

There are also some online tools that allow me to include extra payments in the calculations. Should I put the down payment as an extra payment in year one? Or should it be subtracted from the loan amount?

Any help is appreciated.

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