Loan Interest Payment Calculator and Formula

This loan interest payment calculator estimates a fixed monthly payment and the total interest paid over the loan term. Enter the amount borrowed, annual percentage rate (APR), and term in years; the results show the scheduled payment and interest cost under the stated assumptions.

Formula

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

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

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

Total interest is calculated as (monthly payment × n) − P. The calculator uses the unrounded payment inside its displayed payment formula, rounds the payment shown to cents, and calculates total interest using that displayed payment. This makes the example easy to follow, though cents-rounding can create a small difference from a lender’s final schedule.

Worked Example

Using the calculator’s default inputs: principal P = $20,000, APR = 8%, and term = 5 years.

1. Convert the annual rate to a monthly decimal: r = 8 ÷ 1200 = 0.0066667.
2. Convert the term to payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = $405.53 per month, rounded to cents.
4. Calculate total interest using the displayed payment: $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

• The interest rate is fixed for the entire term.
• Payments are equal monthly payments made at the end of each monthly period.
• Interest compounds monthly at APR ÷ 12.
• The calculation excludes fees, taxes, insurance, PMI, and escrow; these are not calculator inputs.

What an Interest Payment Means

A loan payment can contain both interest and principal. Interest is the charge calculated on the outstanding balance for borrowing money; principal is the portion that reduces the amount still owed. The payment amount is not necessarily all interest, and it does not usually stay divided in the same way throughout an amortizing loan.

At the beginning of a standard fixed-rate loan, the balance is largest, so more of each payment goes toward interest. As principal is repaid, the balance falls and the interest portion generally shrinks. The scheduled payment stays level in this calculator, while the principal portion grows over time. This pattern is called amortization.

For example, at the start of the sample loan, one month’s interest on $20,000 at 8% APR is about $133.33 ($20,000 × 0.08 ÷ 12). The first $405.53 payment therefore includes about $133.33 of interest, with the remainder reducing principal, subject to the lender’s calculation and rounding conventions.

How to Use and Read the Estimate

Enter the amount financed rather than the price of an item if a down payment or trade-in reduces the borrowing. Use the APR shown in the loan disclosure when available, and enter the repayment term in years. The result is a mathematical estimate for a regular, fully amortizing loan—not a payoff quote or a promise of the amount a lender will collect.

• Monthly payment: the estimated fixed payment needed to repay principal and interest over the entered term.
• Total interest: the estimated interest over all scheduled payments, not including excluded costs.
• Total of scheduled payments: payment multiplied by the number of months. It includes repayment of principal as well as interest.

For a rough total outlay under these assumptions, add the principal to the interest result. That amount excludes any fees or other charges not represented in the inputs. A longer term generally spreads repayment across more months; at the same principal and APR, it changes both the scheduled payment and the total interest. The calculator does not determine which term is suitable for any individual.

APR, Interest Rate, and Common Calculation Errors

An interest rate describes the price of borrowing, while APR is a standardized annual measure that may incorporate certain borrowing costs depending on the product and applicable disclosure conventions. This calculator treats the entered APR as a nominal annual rate divided evenly across 12 months. A lender’s actual payment schedule may use different timing or calculations, so use the disclosed payment figures for an exact account-specific amount.

• Do not enter 8 instead of 0.08 in the APR field. The field expects a percentage, such as 8 for 8%.
• Do not confuse years and months. A five-year term means 60 monthly payments in this formula.
• Do not interpret interest as the whole payment. Scheduled payments normally repay principal as well as interest.
• Do not assume every loan is fixed-rate or monthly. Variable rates, irregular payment dates, interest-only periods, and other structures need a different calculation.

Limits and Other Loan Costs

The estimate assumes the full principal is borrowed at the start and repaid through equal monthly installments, with no missed or extra payments. It does not model a changing rate, late charges, payment holidays, fees added to the balance, a final balloon payment, or a lender’s day-count method. If any of these apply, the actual balance and interest can differ.

Extra principal payments can reduce the balance on which later interest is calculated, but their timing and treatment depend on the loan terms. This calculator does not include extra payments or estimate a payoff date after them. For a current balance, payoff amount, or revised schedule, use the lender’s account information because accrued interest and transaction timing matter.

Frequently Asked Questions

How do I calculate interest on a loan payment?
For a standard amortizing loan, calculate the monthly payment from principal, monthly rate, and number of payments. To find the interest part of a particular payment, multiply the balance before that payment by the monthly rate; the rest of the payment reduces principal, subject to the loan’s terms.

Is the monthly payment all interest?
No. A typical fully amortizing payment includes interest and principal. The interest share is usually larger early in the schedule and declines as the principal balance is paid down.

Does APR equal the monthly interest rate?
No. In this calculator, the monthly rate is APR divided by 12 and then by 100 to convert a percentage to a decimal. APR itself is an annual figure.

Why might my lender’s payment differ?
The lender may include costs, use different payment dates or rounding, or apply a rate or repayment structure that the calculator does not model. Compare the entered principal, APR, term, and disclosed schedule, and ask the lender for its exact figures.

Does a longer term reduce total interest?
Not necessarily. For the same principal and APR, extending repayment generally lowers the scheduled monthly payment but adds more payment periods, which can increase total interest under the fixed-rate assumptions used here.

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

Related

• First Stripe Payment: What to Expect
• First Payment Systems: Origins of Money and Trade
• First Payment Solution Calculator and Loan Basics

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 | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2