Loan APR Interest Calculator and Payment Formula

This loan APR interest calculator estimates the monthly payment and total interest for a fixed-rate, fully amortizing loan. Enter the amount borrowed, annual APR, and term in years; the results show the scheduled payment and the interest paid over the term.

Formula

The calculator uses the standard fixed-payment loan formula. It converts the annual percentage rate to a monthly rate, calculates a level payment that pays interest and principal over the term, rounds that payment to cents, and estimates total interest from the rounded payment.

• p = starting loan principal, in dollars.
• apr = annual percentage rate, entered as a percentage per year.
• r = monthly rate as a decimal: apr / 1200.
• n = number of monthly payments: yrs × 12.
• pmt = monthly payment in dollars: round[p × r / (1 − (1 + r)⁻ⁿ), 2].
• int = estimated total interest in dollars: pmt × n − p.

The APR is divided by 1,200 because the input is a percent per year and the schedule is monthly: divide by 100 to express it as a decimal, then by 12 for a monthly rate. This is the calculator’s stated convention; loan disclosures can use different details or include charges that change the effective borrowing cost.

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 decimal rate: 8 / 1200 = 0.0066667.
2. Convert the term to payments: 5 × 12 = 60 months.
3. Substitute into the payment formula: $20,000 × 0.0066667 / [1 − (1.0066667)⁻⁶⁰].
4. The unrounded payment is about $405.53, so the monthly payment rounded to cents is $405.53.
5. Using that rounded payment, total scheduled payments are $405.53 × 60 = $24,331.80.
6. Estimated total interest is $24,331.80 − $20,000 = $4,331.80.

Small differences can arise if another calculator keeps additional precision in each payment rather than using the cent-rounded payment for the total. This calculator explicitly uses the displayed monthly payment for its interest estimate.

Assumptions

• The interest rate is fixed for the entire term.
• Payments are equal monthly payments, made at the end of each monthly period.
• Interest is modelled monthly at APR divided by 12.
• The calculation excludes fees, taxes, insurance, PMI, escrow, late charges, and any extra or missed payments.

What APR Means for a Loan

APR, or annual percentage rate, is a yearly measure associated with the cost of borrowing. It is not the same thing as the amount of interest paid in dollars. The calculator needs both the APR and the principal to estimate payments, and the loan term determines how many payments spread repayment across time.

For a given principal and fixed APR, a longer term generally produces a lower scheduled monthly payment but more payments overall. That can mean more total interest under this formula. A shorter term generally concentrates repayment into larger monthly payments while reducing the number of months during which interest accrues. These are mathematical effects, not a judgment about which term is suitable for any person.

APR and the periodic interest rate also should not be treated as interchangeable. Here, the monthly rate is calculated as APR divided by 12 and 100. A lender’s APR disclosure may reflect the loan’s rate and certain charges under applicable disclosure conventions; the calculator does not determine those charges or reproduce a lender’s disclosure.

How to Use and Read the Results

Enter the amount financed, the APR shown in the lender’s offer or disclosure, and the loan term in years. The input limits are calculator safeguards, not statements about what any lender offers. If the term is stated in months, divide it by 12 before entering it; for example, 36 months is 3 years.

• Monthly payment is the scheduled principal-and-interest amount under the assumptions above. It does not include expenses the calculator has no inputs for.
• Total interest is the estimated interest across all scheduled payments, calculated after rounding the monthly payment to cents.
• Total paid can be checked by adding the principal to total interest. For the example, $20,000 + $4,331.80 = $24,331.80.

Use the actual principal, APR, and repayment term from the loan documents for a closer estimate. If fees are financed into the balance, the principal entered should reflect the amount actually financed; otherwise, the result will not account for them. A lender’s payment can also differ because of payment dates, rounding practices, variable rates, or other contract terms.

What This Estimate Leaves Out

This is a mathematical estimate for a standard, fully amortizing loan: each regular payment covers the period’s interest and reduces principal, and the balance is scheduled to reach zero after the final payment. It does not model a variable rate, balloon payment, interest-only period, deferred payments, irregular payment dates, or a changing payment schedule.

It also does not calculate fees, taxes, insurance, PMI, escrow, or other charges. APR figures may account for certain borrowing costs, but entering an APR does not add those costs to the payment as separate cash amounts. Check the lender’s itemized disclosure for the actual amount due, payment schedule, included charges, and any conditions that could change the amount.

A common misconception is that multiplying the original principal by APR and the number of years gives the loan’s total interest. That simple multiplication ignores the declining balance as principal is repaid. The amortizing-payment formula instead calculates interest on the remaining balance each period, within its monthly-rate and timing assumptions.

Frequently Asked Questions

How do I calculate loan APR interest?
For a fixed-rate amortizing loan, convert APR to a monthly decimal rate, calculate the level monthly payment, then subtract the principal from all scheduled payments combined. This calculator uses the cent-rounded payment for the total-interest estimate.

Is APR the same as the monthly interest rate?
No. APR is entered as a yearly percentage. In this calculation, the monthly decimal rate is APR divided by 1,200. A lender’s APR disclosure may also reflect certain costs, so it is not necessarily identical to the note’s stated interest rate.

Does the monthly payment include fees or insurance?
No. The result includes estimated principal and interest only. Fees, insurance, taxes, PMI, and escrow are not included because they are not inputs to this calculator.

Why does my lender’s payment differ?
The contract may use different dates, rounding, charges, payment timing, or rate terms. Compare the calculator’s assumptions with the lender’s payment schedule and disclosure rather than treating the estimate as the contractual amount.

Can I use this for a variable-rate loan?
Only as a snapshot for a period with a specified rate and fixed payment assumptions. It cannot predict later rate changes or recalculate a changing schedule.

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