I'm in the classic 'pay extra on the house vs invest' argument with my partner (not the subject of this question) and I'm trying to understand what exactly happens when I pay extra on a mortgage. I have my amortization schedule that I've reproduced in Excel and I understand the math behind how the principal and interest is calculated and the change in allocation over the years. I also see what happens when I plug in an extra $X monthly using online calculators.
What I don't understand is what actually happens to the amortization table and the distribution between principal and interest payments.
I assumed that any extra payments were just 'saved' and once the principal was equal to the saved payments, the loan terminated and the sum of the skipped interest payments was my savings. However, that's not what the calculators are telling me and I want to understand why.
My (incorrect) understanding is as follows:
A hypothetical 30-year mortgage with 4% interest on $300,000 (ignoring all additional costs) would result in a monthly payment of $1,432.25. I then assumed that if I paid an extra $100 per month every month from the start of the mortgage, then on the 335th payment I would have a balance of $34,300.03 and a 'saved' $33,500, so I'd pay $800.03 to pay off the mortgage and my savings would be the amortized interest payments from months 336-360 (minus a bit from the partial 336th payment) for a savings of ~$1,506. The calculator I'm using is telling me that I'd reach payoff at month 318 and save $28,746. While that's obviously much better, it won't show me the underlying calculations.