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So I recently wrote my loan provider on whether the extra online payments I was making were applied directly to principal and it turns out they were not, they were just treating it like extra pre-payments that applied toward principal and interest.

It looks like this answer provides the formula for extra payments that directly apply toward the principal.

But what is the formula for extra payments (those pre-payments that were not directly paying off principal) that pay off both principal and interest? I'm trying to calculate how much money I would have saved between the 2 methods.

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    Prepaying future payments does not save you anything. You just would not have a payment for a while until the next due date.
    – void_ptr
    Commented Nov 7, 2023 at 6:13
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    As others answers have said, distinguish between prepaying and paying additional principal. Not all loans will let you do so, but paying down the principal faster is what would save you money. Prepaying, by comparison, might save you from a late-payment fee but otherwise doesn't affect how much you will pay over the course of the loan.
    – keshlam
    Commented Nov 7, 2023 at 7:46
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    It might be a misinterpretation of your question. They might have meant that your "extra" payment will still pay the accrued interest at the time, plus some principal, but then your "regular" payment would have mush less interest, and end the end you'd be at roughly the same spot as if your original payment went completely to principal. If that's the case then treating it as an all-principal payment would get you pretty close; otherwise you'd have to build an amortization schedule to see the true effect.
    – D Stanley
    Commented Nov 7, 2023 at 14:18
  • @void_ptr This comment should just be the answer.
    – Grade 'Eh' Bacon
    Commented Nov 7, 2023 at 14:46
  • @DStanley I think you might be right. I made 2 extra payments and then the due date of my next regularly scheduled amortized payment is due 2 months from those payments. So now I'm thinking each "extra payment" they applied toward the regular amortized payment and then the rest went towards the principal.
    – Nona
    Commented Nov 7, 2023 at 18:39

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they were just treating it like extra pre-payments that applied toward principal and interest.

You will need to get a list of the payments and balances from the company handling the loan. You need to get this to understand how those extra payments were applied.

After a number of extra payments you are no longer following the original amortization schedule.

But what is the formula for extra payments (those pre-payments that were not directly paying off principal) that pay off both principal and interest? I'm trying to calculate how much money I would have saved between the 2 methods.

I would turn the information from the lender into a spreadsheet and then model future payments to see how they change compared to the original schedule.

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