What is the breakeven point for a down payment vs cash?

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I want 150k house. I have 150k cash. Assume S&P yields 7%. Assume interest rate is 7%. Assuming all of that information is exactly true and there's no other factors. Is the most optimal choice to put the least amount down as possible. And then put the cash in the S&P and take annual withdrawals to pay for it? I keep asking chatgpt but it gives me different answers constantly

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What is the breakeven point for a down payment vs cash?
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