How it’s calculated
Each monthly payment first covers that month's interest on the remaining balance; the rest repays principal. Early payments are mostly interest, later ones mostly principal. The balance after k payments has a closed form, so any year can be summarized without listing every row.
Example (OpenStax Principles of Finance 8.3): $140,000 over 20 years at 3.6% gives a payment of about $819.16. Month 1 interest is 140,000 × 0.003 = $420.00 and principal $399.16, leaving $139,600.84. Total interest over the loan is about $56,597.
Real loans round each payment to the cent, so the calculator also runs a cent-rounded schedule: every payment is the rounded amount, each month's interest is rounded to the cent, and the final payment is adjusted to clear the exact remaining balance. Lender schedules may still differ by a few cents (day-count rules, rounding method). At 0% interest every payment is simply the loan ÷ number of payments. Taxes, insurance and fees are not included.
Frequently asked questions
Why is so little principal paid in the first years?
Interest is charged on the balance, which is largest at the start. As the balance falls, less of each payment goes to interest and more to principal.
How do extra payments change the schedule?
Extra principal reduces the balance immediately, so every later month accrues less interest and the loan ends early. Check for prepayment penalties first.
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Sources
- Principles of Finance, 8.3 Loan Amortization — OpenStax
- Contemporary Mathematics, 6.8 The Basics of Loans — OpenStax
- How does paying down a mortgage work? — Consumer Financial Protection Bureau
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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