Amortization is the process of paying off a loan in regular instalments that cover both the interest and a slice of the original amount borrowed (the principal). Every payment is the same size, but its makeup changes: early payments are mostly interest, late payments are mostly principal. Work through your own loan with the Amortization Calculator and the full amortization table it produces.
The payment formula
For a fixed-rate loan, the level monthly payment is
M = P × r × (1 + r)^n / ((1 + r)^n − 1)
where P is the amount borrowed, r the monthly interest rate (annual rate divided by 12) and n the number of monthly payments.
Example: borrow $200,000 at 6.00% a year for 30 years. Here r = 0.06 / 12 = 0.005 and n = 360, which gives M = $1,199.10 a month.
What each payment is made of
Each month the interest is the remaining balance times the monthly rate. The rest of the payment reduces the principal, and the balance falls, so next month's interest is a little lower and a little more of the same payment goes to principal:
| Month | Interest | Principal | Balance after |
|---|---|---|---|
| 1 | $1,000.00 | $199.10 | $199,800.90 |
| 2 | $999.00 | $200.10 | $199,600.80 |
| 3 | $998.00 | $201.10 | $199,399.71 |
| 120 | $838.66 | $360.44 | $167,371.45 |
| 180 | $712.92 | $486.18 | $142,097.69 |
| 240 | $543.31 | $655.79 | $108,007.17 |
| 360 | $5.97 | $1,193.14 | $0.00 |
In month 1 the interest is $200,000 × 0.005 = $1,000.00, leaving only $199.10 to reduce the debt. After 15 years the same payment is already $486.18 principal. Over the whole loan you pay about $231,676.38 in interest on top of the $200,000, so you repay roughly $431,676.38 in total.
The effect of paying extra
Any extra money goes straight to principal, which stops interest accruing on that part for the rest of the loan. Adding just $100 a month to the example loan:
- ends it after 295 payments (24 years 7 months) instead of 360, 5 years 5 months sooner;
- cuts total interest from $231,676.38 to $182,537.97, a saving of about $49,138.41.
See how much a lump sum or extra payment saves you with the Mortgage Payoff Calculator.
Term and rate: the two big levers
- A shorter term costs more per month but far less interest overall.
- A lower rate reduces both. On this loan, a rate of 5.00% instead of 6.00% lowers the monthly payment by about $125.
- Because interest is front-loaded, early extra payments save much more than late ones.
Common mistakes and caveats
- Confusing the interest rate with the APR. The APR includes certain fees and is the better yardstick for comparing offers; see the APR Calculator.
- Forgetting everything else in a housing payment. A mortgage payment often also includes property tax, insurance and sometimes mortgage insurance, none of which amortize. Use the Mortgage Calculator to see the full monthly cost.
- Assuming extra payments always apply to principal. Tell your lender explicitly, and check for prepayment penalties in the contract.
- Adjustable-rate loans. The payment changes when the rate resets, so a schedule is only a projection.
- Thinking amortization is only about loans. Businesses also amortize intangible assets such as patents, spreading the cost over their useful life.
For one-off loans of any kind, use the Loan Calculator. Related terms: Amortization, Principal, APR and Escrow.