Amortization in one paragraph
With a fixed rate amortizing loan (most personal loans, car loans and mortgages), the payment is the same every month. Each month the lender charges interest on what you still owe: the annual rate divided by 12, times the balance. Whatever is left of your payment after that interest goes to the principal and lowers the balance. Next month the balance is smaller, so the interest is smaller and more of the same payment goes to principal. After the last payment the balance is exactly zero.
The loan calculator on this page uses this standard method. Enter the Loan amount, the Annual interest rate and the Term in years or months to see the Monthly payment, Total interest and Total paid, and open the Payment schedule by year or by month.
Try it here: Loan Calculator
Open the full tool pageThe monthly payment formula
The payment M for a loan amount P, a monthly rate r (annual rate divided by 12, as a decimal) and n monthly payments is: M = P × r / (1 minus (1 + r) to the power of minus n). For 20,000 at 6 percent over 5 years: r = 0.06 / 12 = 0.005 and n = 60. Then (1.005) to the power of minus 60 is about 0.7414, so 1 minus that is 0.2586, and 20,000 × 0.005 / 0.2586 gives 386.66.
Multiply the payment by the number of payments to get the total paid: 386.66 × 60 = 23,199.36. Subtract the loan amount and the total interest is 3,199.36. In a spreadsheet the same payment comes from =PMT(6%/12, 60, -20000). If the rate is 0, the formula does not apply and the payment is simply P / n.
Example amortization schedule
Here is the 20,000 loan at 6 percent over 60 months. In the first month the interest is 20,000 × 0.005 = 100.00, so 286.66 of the payment reduces the balance. By the last month the interest is only 1.92 and almost the whole payment is principal.
| Payment | Interest | Principal | Balance after payment |
|---|---|---|---|
| Month 1 | 100.00 | 286.66 | 19,713.34 |
| Month 2 | 98.57 | 288.09 | 19,425.25 |
| Month 12 | 83.83 | 302.82 | 16,463.94 |
| Month 24 | 65.16 | 321.50 | 12,709.78 |
| Month 36 | 45.33 | 341.33 | 8,724.07 |
| Month 48 | 24.27 | 362.38 | 4,492.53 |
| Month 60 | 1.92 | 384.73 | 0.00 |
The same loan year by year
Grouped by year, the shift from interest to principal is easy to see. In year 1 you pay 1,103.81 of interest; in year 5 only 147.34. This is why paying off a loan early saves much more in the first years than in the last ones. The By year view of the calculator shows exactly this table for your own numbers, and Download CSV saves the schedule for Excel or Google Sheets.
| Year | Interest paid | Principal paid | Balance at year end |
|---|---|---|---|
| 1 | 1,103.81 | 3,536.06 | 16,463.94 |
| 2 | 885.71 | 3,754.16 | 12,709.78 |
| 3 | 654.16 | 3,985.71 | 8,724.07 |
| 4 | 408.33 | 4,231.54 | 4,492.53 |
| 5 | 147.34 | 4,492.53 | 0.00 |
| Total | 3,199.36 | 20,000.00 |
How the term and the rate change the cost
A longer term lowers the monthly payment but raises the total interest, because you owe money for longer. A lower rate reduces both. For the 20,000 loan, stretching from 5 to 7 years saves about 94 a month but adds more than 1,300 of interest.
The effect is much larger on a mortgage. A 200,000 loan at 6 percent costs 1,199.10 a month over 30 years with 231,676 of interest, more than the amount borrowed. Over 15 years the payment is 1,687.71, but the interest drops to 103,788. At 5 percent over 30 years the payment is 1,073.64 and the interest 186,512; at 7 percent it is 1,330.60 and 279,018.
| Loan of 20,000 | Monthly payment | Total interest |
|---|---|---|
| 6%, 3 years | 608.44 | 1,903.79 |
| 6%, 5 years | 386.66 | 3,199.36 |
| 6%, 7 years | 292.17 | 4,542.37 |
| 4%, 5 years | 368.33 | 2,099.83 |
| 8%, 5 years | 405.53 | 4,331.67 |
Extra payments and paying off early
Any extra money paid towards principal skips the interest it would have generated for the rest of the term. On the 200,000 mortgage at 6 percent over 30 years, paying 100 more every month ends the loan after 295 payments instead of 360 (about 5 years early) and cuts the interest from 231,676 to about 182,538, a saving of roughly 49,000. On the 20,000 car loan, 50 more a month finishes 7 months early and saves about 430.
The calculator does not have a separate field for extra payments, but you can model a one time prepayment: read the balance in the schedule at the month you plan to pay, subtract the prepayment and enter the result as a new loan with the remaining months. Compare the new total interest with what is left in the original schedule.
Before paying extra, check the contract. Some loans charge a prepayment fee, and some lenders apply extra money to the next payments instead of the principal unless you ask. Ask for the extra amount to reduce principal and decide whether you want a shorter term or a lower payment.
APR, fees and other loan types
The nominal annual rate is used to calculate interest. The annual percentage rate (APR) also includes the main fees and charges spread over the term, so it is the better number for comparing offers. If you enter the APR as the rate in the calculator, you get a payment and total cost closer to the real cost of borrowing. Insurance, taxes and account fees may still be charged on top.
Not every loan amortizes the same way. Some lenders use equal principal payments, where the payment starts high and falls every month. Interest only loans keep the balance unchanged for a period, and balloon loans leave a large final payment. Variable rate loans recalculate the payment when the rate changes. The calculator models the most common case: a fixed rate and equal monthly payments, as an estimate rather than a bank offer.