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I owed about 45k on student loans. I wrote a check for around 10k to get the balance down. What I expected to happen was, for the balance to go down more than 10k, because that 10k would no longer be subject to interest. That didn't happen; the balance remained (before - 10k).
Why's that?
Is the interest a set amount, no matter how fast I pay it off?
Or is the interest not listed in the balance, but taken out of every payment?

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    Please clarify, did the balance not go down at all, or only went down 10k while you expected it to go down more? – Vality Jul 31 '16 at 3:26
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The future interest is not yet a part of the balance you see, it will be added every month.

So next month, less interest will be added to the balance (compared to not paying that larger amount).

What you see in the balance is all principal. Every month, the interest gets added, you payment gets deducted (hopefully it is larger than the interest), and you see the new principal.

For example, with 6% interest per year and 20000 $ balance: you will get 6% / 12 month = 0.5%/month = 100 $ interest added, you pay the minimum of 120 $, so the new total is 20000 + 100 - 120 = 19980 $ (that's why the minimum payment doesn't get you anywhere quickly).

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