Method
Level-payment amortization
Used by Where did my payments go? and by every comparison tool. The worked example below is the same fixture our automated tests check on every release, so this page cannot drift from the code.
The formula
For a loan of principal P, a periodic rate r (the annual rate divided by the number of payments per year) and n payments, the level payment is:
payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
Each period, interest is the remaining balance times r. Whatever is left of the payment reduces the balance. Because the balance shrinks, interest shrinks and the principal share grows, which is why early payments feel slow.
If the rate is zero, the payment is simply P ÷ n.
Worked example
$20,000.00 at 18% for 60 monthly payments, no fees, first payment one month after disbursement. Monthly rate r = 1.5%. Payment = $507.87.
| Month | Payment | Interest | Principal | Balance after |
|---|---|---|---|---|
| 1 | $507.87 | $300.00 | $207.87 | $19,792.13 |
| 2 | $507.87 | $296.88 | $210.99 | $19,581.14 |
| 3 | $507.87 | $293.72 | $214.15 | $19,366.99 |
| 4 | $507.87 | $290.50 | $217.36 | $19,149.63 |
| 5 | $507.87 | $287.24 | $220.62 | $18,929.01 |
| 6 | $507.87 | $283.94 | $223.93 | $18,705.07 |
| 7 | $507.87 | $280.58 | $227.29 | $18,477.78 |
| 8 | $507.87 | $277.17 | $230.70 | $18,247.08 |
| 9 | $507.87 | $273.71 | $234.16 | $18,012.92 |
| 10 | $507.87 | $270.19 | $237.67 | $17,775.24 |
| 11 | $507.87 | $266.63 | $241.24 | $17,534.00 |
| 12 | $507.87 | $263.01 | $244.86 | $17,289.14 |
After 12 payments: paid $6,094.42, of which $2,710.86 reduced the balance and $3,383.56 was interest. Balance remaining $17,289.14, about 86% of the original loan.
Roughly 86% of the original principal remains after one year. Values use the unrounded payment; a live payoff quote can differ because of daily interest, actual payment dates and fees.
Rounding
Two modes exist in the engine. Exact keeps the payment unrounded inside the calculation and is used for fair comparisons between offers and for this page. Per-period rounds the payment and each month's interest to the cent, the way a servicing system posts them, and lets the final payment absorb the difference. On the example above the two modes differ by a few cents over a year.
What this method does not cover
- Daily simple-interest loans, where the interest charged depends on the exact day each payment arrives.
- Precomputed-interest loans, where the total interest is fixed at signing and an early payoff uses a rebate rule from the contract.
- Fees, late charges, deferments and extra payments. The comparison tools handle fees separately.
Reviewed 5 September 2026. Corrections are dated on this page.