Question about how mortgage prepayment affects amortization schedule.?

So I’m buying my first house, its an FHA loan, and the biggest thing on my mind is figuring out how to pay as little interest as possible over the years. I’m buying a less expensive house that I could afford, so that I can have money left over to prepay on the principal as often as possible, and get the house paid off much quicker than 30 years. ( I know alot of people probably think, its my first house, I’m going to move soon, upgrade, etc, but I doubt it. I rarely move, I’ve been in the same 5 mile radius my whole life, I plan to be in this house for a long time)

Right now I’ve already got my minimum down payment/closing costs. I’ve also got enough money for an emergency fund. Then on top of that I’ve got around $ 4K extra that I can apply to the principal. Now since I’m not completely familiar with how the whole amortization schedule works, I’m wondering which way I’d be better off.

A) Just applying that extra directly to my down payment up front, which will lower my monthly payment by about $ 20 a month, but will still be amortized at 30 years (as far as I know).

B) Just putting down the minimum down payment, and then in about a month applying that $ 4K to the principle. That way the loan has already been amortized, and (if my thinking is right), I’ll be getting a jump start through the amortization schedule, so that on all my future payments, more of the payment will be going straight to principal and less towards interest. And in effect taking a year or so off the end of the loan. (that’s how i think it works, although I don’t fully understand how the ammortization works, so that’s why I’m asking the question)

So with overall interest savings throughout the years in mind, which is a better option, or are they both going to pretty much be the same?

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