Loan Amortization Calculator: Payments and Interest

A loan amortization calculator shows the level monthly payment on a fixed-rate loan and estimates how much interest you pay over its full term. Enter the loan amount, annual percentage rate (APR), and term in years to see the monthly payment and total interest.

Formula

This calculator uses the standard level-payment formula for a fixed-rate loan with monthly payments:

Monthly payment = round(P × r ÷ [1 − (1 + r)⁻ⁿ], 2)

• P is the starting loan principal, in dollars.
• r is the monthly interest rate, calculated as APR ÷ 1,200. For an 8% APR, r is 0.08 ÷ 12, or about 0.006667 per month.
• n is the total number of monthly payments, calculated as the term in years × 12.
• round(…, 2) rounds the payment to the nearest cent.

Total interest is calculated as the rounded monthly payment multiplied by the number of payments, minus the original principal: Total interest = monthly payment × n − P. It assumes every scheduled payment is made on time and the balance reaches zero at the end of the term. Actual loan servicing can differ because of payment dates, rounding methods, fees, or loan terms that are not represented here.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and a five-year term:

1. Convert the APR to a monthly rate: 8 ÷ 1,200 = 0.0066667.
2. Find the number of payments: 5 × 12 = 60 months.
3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = approximately $405.53 per month after rounding to cents.
4. Calculate total interest using that rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

The estimated results are a monthly payment of $405.53 and total interest of $4,331.80. The payment amount is rounded before calculating interest, so the displayed figures follow the same convention.

Assumptions

• The interest rate is fixed for the entire term.
• Payments are equal monthly payments, made at the end of each monthly period.
• Interest accrues monthly at APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, late charges, and extra payments are not included.

What Loan Amortization Means

Amortization is the process of paying down a debt through scheduled installments. Each payment covers interest accrued since the previous payment and reduces the remaining principal. Early in a standard amortizing loan, the balance is relatively large, so a larger share of a level payment goes to interest. As principal falls, the interest portion generally declines and more of the same payment goes toward principal.

An amortization schedule lays out that process period by period. For each month, it typically shows the opening balance, payment, interest charged, principal repaid, and closing balance. This calculator summarizes the scheduled payment and total interest; it does not display the full monthly schedule.

How to Read the Results

The monthly payment is the estimated amount needed each month under the stated assumptions. Total interest is the sum of the interest implied by those scheduled payments over the full term. It is not the total amount repaid: adding the original principal to the displayed interest gives the estimated total of payments. With the example inputs, that is $20,000 + $4,331.80 = $24,331.80.

Changing one input changes the result. A larger principal generally raises the payment and total interest. A longer term usually lowers the required monthly payment but increases the number of months over which interest accrues. A higher APR raises the monthly interest rate and generally increases both the payment and total interest. These are mathematical relationships, not a judgment about a particular loan.

Common Misunderstandings and Limits

APR and the monthly rate are not interchangeable. The formula converts a nominal annual APR to a monthly rate by dividing by 12; entering 8 for an 8% APR is correct because the calculator performs the percentage conversion itself. Do not enter 0.08 unless the input explicitly requests a decimal rate.

This estimate also does not necessarily equal a lender’s quoted amount. A disclosed payment may include loan-specific charges or use a different payment schedule, and adjustable rates can change over time. If a payment is rounded to cents each month, the final installment can be slightly different from the others to clear the remaining balance. The calculator uses a single rounded payment for its total-interest estimate, so small differences from a lender’s amortization schedule are possible.

Extra principal payments are not included. They can change the balance path and reduce future interest, but the outcome depends on when payments are credited and how the loan applies them. To model those details accurately, use the loan’s actual terms and payment history rather than treating this basic fixed-payment estimate as a complete payoff schedule.

Frequently Asked Questions

What does a loan amortization calculator calculate?
It estimates a fixed monthly payment and the total interest implied by the principal, APR, and term entered. This calculator does not produce a month-by-month schedule.

How much of each payment goes to principal?
The principal portion is the payment minus the interest for that period. Interest is based on the outstanding balance and the applicable periodic rate; as the balance declines, the principal portion of a level payment generally grows.

Does a longer loan term reduce total interest?
Not necessarily. A longer term generally spreads repayment over more payments and may reduce the monthly payment, but this formula usually produces more total interest when principal and APR stay the same.

Does this calculator include fees or extra payments?
No. It assumes scheduled monthly payments on a fixed-rate loan and excludes fees and extra principal payments. Check the lender’s figures for charges and the loan’s rules for payment application.

Why might the result differ from my lender’s payment?
The lender may include charges, use different timing or rounding, or apply a rate or repayment structure not captured here. Compare the inputs and assumptions with the lender’s loan disclosure.

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

Related

• Term Loan vs Revolving Loan: Key Differences
• Term Loan EMI Calculator and How It Works
• Term Loan Facility: Meaning, Structure and Key Terms

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