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Why can’t I just compare my current payment to the proposed payment and figure out my net benefit?

Why can’t I just compare my current payment to the proposed payment and figure out my net benefit?

You could just compare just the two payments if you wanted to find out your cash flow savings, but the current and proposed loans may have two different amortizations. Let’s say you have a 15-year mortgage currently and you are comparing to a 30-year mortgage.
If everything else is the same (interest rate, loan amount, etc) except for the amortization your interest savings per month would be $0 but, you are going to show a cash flow savings because of the longer amortization.