Interest Rate APR Calculator and Loan Payment Formula

This APR calculator estimates the monthly payment and total interest on a fixed-rate, fully amortizing loan from its amount, annual percentage rate, and term. Enter the figures from a lender’s loan disclosure to see an arithmetic estimate; the result does not include fees or other borrowing costs that may affect the disclosed APR.

Formula

The calculator uses the standard fixed-payment loan formula. It converts APR to a monthly rate, calculates the payment that would repay the starting balance over the selected number of monthly payments, rounds that payment to the nearest cent, and subtracts the amount borrowed from the sum of the payments to estimate total interest.

• P is the loan principal, or amount borrowed, in dollars.
• APR is the annual percentage rate entered as a percentage, such as 8 for 8% per year.
• r is the monthly rate, calculated as APR ÷ 1,200. For an 8% APR, r = 0.08 ÷ 12, or 0.0066667 per month.
• n is the number of monthly payments, calculated as years × 12.
• M is the monthly payment in dollars.

In symbols, M = P × r ÷ [1 − (1 + r)⁻ⁿ]. The displayed payment is rounded to cents. Estimated total interest is M × n − P, using that rounded payment. This convention reflects the scheduled payment amount, though an actual lender may adjust the final payment slightly to account for cents-level rounding or its payment schedule.

Worked Example

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

1. Convert the APR to a monthly rate: r = 8 ÷ 1,200 = 0.0066667.
2. Convert the term to payments: n = 5 × 12 = 60.
3. Apply the formula: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = $405.53 per month, rounded to cents.
4. Estimate total interest: $405.53 × 60 − $20,000 = $4,331.80.

The calculator therefore shows a monthly payment of $405.53 and estimated total interest of $4,331.80. Multiplying the rounded payment by all 60 installments gives total scheduled payments of $24,331.80; subtracting the $20,000 principal gives the stated interest estimate.

Assumptions

• The interest rate stays fixed for the full loan term.
• Payments are equal, made monthly, and paid at the end of each monthly period.
• Interest is modelled monthly at APR ÷ 12.
• Fees, taxes, insurance, PMI, escrow, and any separate charges are not included.

What APR Means

APR stands for annual percentage rate. It is a yearly percentage used to describe borrowing cost. For a loan, the APR disclosed by a lender may reflect certain finance charges as well as the interest rate, depending on the loan and the disclosure method. That means APR and the stated interest rate are related but are not necessarily identical.

This calculator uses the entered APR as though it were the loan’s nominal annual rate, divided evenly into 12 monthly periods. It does not independently reconstruct a lender’s APR from fees, payment dates, or other charges. If the APR includes costs that are paid upfront rather than added to the balance, the payment on the principal alone will not show those costs. Use the lender’s disclosure to understand the figures and terms actually offered.

How to Use and Read the Estimate

Enter the amount financed, the APR as a percentage, and the term in years. For example, enter 8 for an 8% APR, not 0.08. The loan amount must be positive; the APR field accepts 0.01% through 100%, and the term accepts 0.0833 through 50 years. The minimum term is approximately one month.

The monthly payment is the scheduled principal-and-interest amount under the fixed-payment assumptions. The total-interest figure is the sum of those rounded scheduled payments minus the initial principal. It is not the total cost of ownership and does not include charges outside the model. A longer term generally spreads repayment over more payments; the effect on a specific loan depends on its inputs and the assumptions above.

To make a meaningful estimate, use matching figures: compare the same amount financed, APR basis, and repayment term. If a lender provides a monthly payment that differs, check whether the quoted amount includes fees, insurance, a balloon payment, a different first-payment date, or a rate that can change. The calculator is not an offer, approval decision, or payment schedule.

Common Limitations and Mistakes

• Confusing APR with the interest rate: APR can account for certain charges, while the interest rate describes interest. This formula treats the APR itself as the monthly-rate basis, so it is an approximation when fees are part of the disclosed APR.
• Entering a decimal instead of a percentage: Enter 8 for 8%, not 0.08. The calculator divides the entered percentage by 1,200.
• Assuming every loan has level payments: Variable-rate loans, interest-only periods, balloon payments, and irregular schedules do not follow this formula throughout their life.
• Ignoring rounding: The monthly payment is rounded to cents before total interest is calculated. A lender may adjust the last installment by a small amount.
• Leaving out financed charges: If a fee is added to the balance, the amount financed may differ from the cash amount received. Enter the relevant financed principal to model the payment, and treat other charges separately.

Frequently Asked Questions

Is APR the same as the interest rate?
Not always. The interest rate is the rate used to calculate interest on the balance; APR is a broader annual cost measure that may include certain finance charges. This calculator uses the entered APR as its rate input and does not separately model fees.

How do I calculate a monthly payment from APR?
Convert APR to a monthly rate by dividing the percentage by 1,200, convert the term to months, and use the fixed-payment formula shown above. The calculator performs those steps and rounds the payment to cents.

Why is my lender’s payment different?
The lender may use a different amount financed, payment timing, rate basis, rounding method, or schedule. The quoted payment may also include items this calculator leaves out. Check the lender’s disclosure for the exact calculation and charges.

Does the total interest include fees?
No. It estimates interest by subtracting principal from the total of the rounded monthly payments. Fees and other charges are not inputs, so they are not included.

Can I use this for a variable-rate loan?
Only as a simplified estimate for a period when one rate applies. A variable rate can change, so future payments and total interest may differ from this fixed-rate calculation.

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

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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