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When I first learned of amortization schedules I was confused by the division of payments into "interest" and "principle". I think I get it now: isn't it that the principle payment goes towards how much of the house you own? I think "how much of the house you own" is referred to as "equity", right?

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You're muddling up two things but you're very close.

Say you buy a house for $100,000. You have $20,000 of your own and you borrow $80,000 from the bank. At that moment you have equity of $20,000. In each payment, some goes to the principal (which started at 80k and will go down over the term of the loan) and some is charged as interest. So, all else being equal, if your mortgage payment this month includes $1000 of principal, your equity increases by $1000.

The thing is, however, that "all else being equal." Because the value of your house can go up (and occasionally down) over the years. If you could sell that house for $110k right now, then your equity is your original 20k, plus the 10k the house has increased, plus whatever you paid down off your mortgage. (Less, to be fair, a bunch of fees and taxes that depend on your location.) So it's more than 30k. If your house goes down and you could only sell it for $90k today, then your equity goes down, too.

At any time your equity is what you can sell the house for, less the principal owing on your mortgage. So lowering the remaining principal does increase your equity. But "how much of the house you own" and "how much you less do you owe on the loan than when you bought the house" are two different things. Related, but different.

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  • When you say "plus whatever you paid down off your mortgage" you're referring only to the principle part, right?
    – user99899
    Commented Jul 8, 2020 at 22:37
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    right, you pay down the principal. The interest just goes to the bank. Commented Jul 8, 2020 at 22:38

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