How Loan Amortization Works
A fixed-rate loan has the same payment every month, yet the share going to interest falls month by month. Here is why, with every number worked out.
The payment formula
M = P × i ÷ (1 − (1 + i)^−n)
- M
- monthly payment
- P
- amount borrowed
- i
- monthly rate = annual rate ÷ 12
- n
- number of payments
The formula finds the single payment that, applied every month, brings the balance to exactly zero after n payments.
Month by month
Take 10,000 borrowed at 6% a year over 12 months. The monthly rate is 0.5% and the payment is 860.66. Each month, interest is 0.5% of the balance still owed; the rest of the payment reduces the balance.
| Month | Payment | Interest | Principal | Balance after |
|---|---|---|---|---|
| 1 | 860.66 | 50.00 | 810.66 | 9,189.34 |
| 2 | 860.66 | 45.95 | 814.71 | 8,374.63 |
| 3 | 860.66 | 41.87 | 818.79 | 7,555.84 |
| 4 | 860.66 | 37.78 | 822.88 | 6,732.96 |
| 5 | 860.66 | 33.66 | 827.00 | 5,905.96 |
| 6 | 860.66 | 29.53 | 831.13 | 5,074.83 |
| 7 | 860.66 | 25.37 | 835.29 | 4,239.54 |
| 8 | 860.66 | 21.20 | 839.46 | 3,400.08 |
| 9 | 860.66 | 17.00 | 843.66 | 2,556.42 |
| 10 | 860.66 | 12.78 | 847.88 | 1,708.54 |
| 11 | 860.66 | 8.54 | 852.12 | 856.42 |
| 12 | 860.70 | 4.28 | 856.42 | 0.00 |
Interest in month 1 is 50.00; by month 12 it has fallen to 4.28, because the balance it is charged on has shrunk. Total interest: 327.96. The last payment differs by a few cents because each month’s interest is rounded to the cent.
Long loans: interest dominates early
On 200,000 at 6% over 30 years the payment is 1,199.10. In the first month 1,000.00 of it is interest and only 199.10 reduces the balance. Over the full term, total interest comes to 231,677.04 — more than the amount borrowed.
What changes the total cost
- The term. A shorter term means higher payments but much less interest, because the balance falls faster.
- The rate. Interest is charged on the outstanding balance every month, so small rate differences add up over long terms.
- Extra payments. Paying more than the scheduled amount goes straight to principal. As arithmetic only: adding 100 a month to the 200,000 example above would repay it in 24 years 7 months instead of 30 years, with total interest of 182,538.19 instead of 231,677.04. Many loans have terms or fees for early repayment, so check the agreement.
Why your lender’s numbers may differ slightly
- Interest may be calculated on actual days in each period rather than one-twelfth of a year.
- Fees, insurance and taxes are often added to the payment or included in the legally disclosed APR.
- Rounding rules for the payment and the final payment vary.