Loan Amortization: Definition, Formula and Example

Loan amortization is the process of repaying a loan through scheduled payments that cover both interest and principal over time. This calculator estimates the fixed monthly payment and total interest from the loan amount, annual percentage rate (APR), and term you enter.

Formula

For a fixed-rate loan with equal monthly payments, the payment is calculated using the standard amortization formula:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 12 ÷ 100.
• n is the number of monthly payments: loan term in years × 12.

The calculator rounds the monthly payment to the nearest cent. It then estimates total interest as the rounded payment multiplied by the number of monthly payments, minus the original principal. Actual loan schedules may differ slightly because of payment dates, lender rounding, fees, or other contract terms.

Worked Example

Using the defaults above, the principal is $20,000, APR is 8%, and the term is 5 years.

1. Convert APR to a monthly decimal rate: 8 ÷ 100 ÷ 12 = 0.0066667.
2. Find the number of payments: 5 × 12 = 60.
3. Substitute into the formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
4. The monthly payment is approximately $405.53 after rounding to cents.
5. Total interest using that rounded payment is $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal and made monthly at the end of each period.
• Interest is modelled monthly, using APR divided by 12.
• Fees, taxes, insurance, mortgage insurance, and escrow are not included.

How Amortization Works

Each scheduled payment is split between interest and principal. Interest for a period is calculated from the outstanding balance and the applicable rate. The amount left after paying that interest reduces the balance. Because the balance generally declines, the interest portion of a fixed payment usually gets smaller over time, while the principal portion grows.

For example, at the start of the illustrated loan, monthly interest is about $133.33 ($20,000 × 0.0066667). From a $405.53 payment, roughly $272.20 therefore goes toward principal. Later, when the balance is lower, less of the same payment is needed for interest. The final payment can differ slightly from the scheduled amount when the lender adjusts for cent rounding.

An amortization schedule lays out this process payment by payment. It commonly shows the payment number or date, payment amount, interest charged, principal repaid, and balance remaining. Such a schedule helps distinguish the amount due each month from the amount that actually reduces the debt.

What the Results Mean

The monthly payment is the formula’s estimated regular payment for principal and interest—not necessarily the full amount a borrower pays each month. A mortgage bill, for instance, may include separately calculated taxes, insurance, or other charges. The total-interest result is the estimated interest paid over all scheduled payments if the loan follows the model and is paid to the end of its stated term.

Term length affects both payment size and cumulative interest. With the same principal and APR, spreading repayment over more months generally lowers the required monthly payment but leaves the balance outstanding longer, so total interest generally rises. A shorter term generally raises the monthly payment and lowers total interest, all else equal. These are mathematical effects, not a judgment about which term fits any particular person.

Extra Payments and Common Misunderstandings

This calculator assumes only the scheduled monthly payment; it does not model extra principal payments, skipped payments, a changing rate, or an early payoff. An extra payment may reduce principal sooner and change later interest, but how it is applied depends on the loan terms and payment handling. To estimate an altered schedule, the balance must be recalculated after each payment using the actual payment dates, rate, and amounts.

• APR is not the monthly rate. For this formula, the monthly rate is APR divided by 1,200, not APR divided by 12 while leaving it as a percentage.
• Payment is not total borrowing cost. The displayed payment covers modeled principal and interest only; fees and other charges are excluded.
• Amortization is not simply a payment split. It describes how the balance is repaid over time, including the changing interest and principal portions.
• Rounding matters. A few cents of rounding each month can make a lender’s final schedule differ from an unrounded mathematical calculation.

When This Estimate Is Useful—and Its Limits

The calculation can help explain a quoted payment, compare hypothetical combinations of principal, APR, and term on a consistent basis, or show why payment size alone does not reveal total interest. Enter the loan’s actual principal, stated APR, and repayment term to model those inputs. Obtain the applicable figures and details from the lender; this calculator does not determine eligibility or account for a lender’s individual method of calculating interest.

The standard formula assumes a fully amortizing loan: if payments are made as scheduled, the modeled balance reaches zero at the end of the term. It does not fit every borrowing arrangement. Interest-only periods, balloon payments, variable rates, irregular payment intervals, deferred interest, or fees financed into the balance can require a different calculation. A displayed result is an estimate rather than a substitute for the contract’s payment schedule.

Frequently Asked Questions

What does loan amortization mean?
It means repaying a loan over time through scheduled payments that cover interest and reduce principal, with the balance declining according to the payment and interest terms.

Does an amortized payment stay the same?
For a fixed-rate loan with equal scheduled payments, the principal-and-interest payment is generally level. The amounts allocated to interest and principal change as the balance falls.

Is amortization the same as interest?
No. Interest is the cost charged for borrowing over a period. Amortization is the repayment process that applies each payment to interest and principal over time.

Why does the early part of a loan payment go mostly to interest?
Interest is calculated on the outstanding balance. That balance is largest near the beginning, so the interest charge takes a larger share of a fixed payment then than it does later.

Does this estimate include taxes or fees?
No. It models principal and interest only. Check the lender’s disclosure for the actual payment schedule and any additional charges.

This result is an estimate; the lender’s disclosure gives the exact figures.

Related

• Bank Loan Amortization Calculator and Payment Formula
• Biweekly Loan Amortization Schedule Calculator
• Balloon Loan Amortization Schedule Calculator

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2