Loan Amortization Calculator

How loan amortization works

On a loan with monthly interest, each payment first covers the interest on what you still owe, at one-twelfth of the annual rate. At 6% that is 0.5% a month, so the first month's interest on $300,000 is $1,500.00. The rest of the payment reduces the balance. The next month's interest is a little smaller, so a little more of the same payment goes to principal. In its answer on amortization and auto loans, the Consumer Financial Protection Bureau (CFPB) puts it this way: "In an amortizing loan, a percentage of your monthly payment is applied to the principal and to the interest. At the beginning of your loan term, more of your payment is generally applied toward the interest rather than the principal."

Amortization formula

r = annual rate ÷ 12          n = years × 12
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)        M = P ÷ n when r = 0
interest_k = B_(k−1) × r      principal_k = M − interest_k
B_k = P × (1 + r)^k − M × ((1 + r)^k − 1) ÷ r
crossover payment = n + 1 − ln 2 ÷ ln(1 + r), rounded up, and at least 1 (r > 0, before rounding to the cent)
P loan amount · r monthly rate · n months in the term · M payment
k payment number · B_k balance after payment k · ln natural logarithm

Worked examples

For a $300,000 loan at 6% for 30 years, the formula gives $1,798.6516 a month, which is paid as $1,798.65.

At the same 6%, a 15-year term costs $2,531.57 a month, $732.92 more. Total interest falls to $155,682.79, which is $191,832.65 less, and principal passes interest at payment 43 instead of 223. That saving is not free money. In effect, the extra $732.92 a month earns the loan's 6%: at that rate, both sets of payments are worth the same $300,000 today. Shorter terms usually come with lower rates too. The CFPB's page on the different kinds of loans says the rate on a shorter term "is usually lower—by as much as a full percentage point." At 5.5% the 15-year payment would be $2,451.25 and the total interest $141,225.11.

A $25,000 car loan at 7.5% for 5 years is 59 payments of $500.95 and a final payment of $500.91, with $5,056.96 of interest. Its first payment is already mostly principal: $344.70 against $156.25 of interest. That is because 60 months is shorter than one doubling time at 7.5%, about 111 payments.

Assumptions and limitations

• The rate is fixed for the whole term. An adjustable-rate loan's payment can change when the rate resets; see the adjustable-rate mortgage calculator.
• Payments are monthly, the first one month after the loan starts. Interest is one-twelfth of the annual rate each month, not figured by the day.
• The payment and each month's interest are rounded to the nearest cent, with half a cent rounded up. The last payment absorbs the rounding, so at high rates over long terms it can be more than twice the others.
• Principal and interest only. Property tax, homeowners insurance and mortgage insurance are paid on top, often through escrow, an account the servicer uses to pay them. As the CFPB's Loan Estimate explainer puts it, your total monthly payment "will typically be more than this amount due to taxes and insurance." Closing costs you finance belong in the loan amount.
• No extra, late or missed payments, fees or prepayment penalties.
• Loan amounts from $100 to $100,000,000, rates from 0% to 100% with up to three decimals, and terms of 1 to 50 years. The $300,000 and 6% defaults are round figures for illustration, not a quote of current rates.
• For your own loan, go by your loan papers: for a mortgage, the Loan Estimate and Closing Disclosure.

These figures are estimates for learning and planning, not financial, tax, legal or investment advice. Terms of use.

What to do with your schedule

Compare terms at the rates you are actually offered. On $300,000, a 15-year loan at 5.5% instead of a 30-year loan at 6% costs $652.60 more a month and $206,290.33 less interest. The 15 vs 30 year mortgage calculator puts two offers side by side.

Shop the rate: on the default loan, a quarter of a percentage point (6% to 6.25%) adds $48.50 a month and $17,460.36 of interest. The CFPB's page on the different kinds of loans advises: "Always compare official loan proposals, called Loan Estimates, before making your decision." The APR calculator shows what fees add.

Check page 3 of your Loan Estimate against this page. On a loan longer than 5 years, "Principal you will have paid off" should match the dollar figure the summary gives for the first 5 years. Add the prepaid interest on page 2, as a share of the loan, to the summary's Total Interest Percentage (115.838% on the default loan). The TIP should be close to that, as the Loan Estimate section shows.

Before you pay extra, check your loan documents for a prepayment penalty. The CFPB's answer on the subject defines it as "a fee that some lenders charge if you pay off all or part of your mortgage early." Then ask the servicer to put the extra toward principal. In its answer on paying interest or principal on an auto loan, the CFPB says, "You may be able to request that your lender or servicer apply more of your payment to your loan’s principal. Check your loan documents first." In the loan extra payment calculator, a one-time $10,000 paid with payment 12 takes 29 months off the default loan and saves $42,805.58 of interest. That $10,000 in effect earns the loan's 6%, as the section on extra payments explains.

Refinancing restarts the schedule. After 5 years you still owe $279,163.14, 93.1% of the loan, and a new 30-year loan's early payments are mostly interest again. The mortgage refinance calculator weighs that against a lower rate.

Frequently asked questions