APR Calculator: Estimate Monthly Loan Payments

This APR calculator estimates the monthly payment and total interest on a fixed-rate loan when you enter the amount borrowed, annual percentage rate, and term. It uses a standard monthly-payment formula; the results are estimates, not a lender’s final disclosure.

Formula

The calculator treats the APR as a nominal annual rate divided into 12 equal monthly periods. It calculates a level payment that amortizes the starting balance over the selected number of months:

• Monthly rate: r = APR / 1200, where APR is entered as a percentage per year and r is a decimal rate per month.
• Number of payments: n = years × 12, in months.
• Monthly payment: payment = P × r / (1 − (1 + r)⁻ⁿ), where P is the loan principal in dollars.
• Total interest: payment × n − P, using the displayed monthly payment rounded to cents.

For the calculator inputs, the loan amount P is in dollars, APR is a percentage, and the term is in years. The monthly payment and total interest are in dollars. The formula assumes payments occur monthly and the rate stays fixed. The monthly rate is not APR divided by 100; it is APR divided by 1200 because the percentage must be converted to a decimal and divided by 12.

Worked Example

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

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

The calculator therefore shows a monthly payment of $405.53 and total interest of $4,331.80 for these inputs. Multiplying the rounded payment by 60 gives total scheduled payments of $24,331.80; subtracting the original $20,000 gives the displayed interest.

Assumptions

• The interest rate is fixed for the full term.
• Payments are equal, made monthly, and begin one month after borrowing.
• Interest is modelled monthly at APR divided by 12.
• The calculation does not include fees, taxes, insurance, PMI, escrow, late charges, or other costs.
• Interest is calculated from the displayed payment rounded to the nearest cent; an actual final payment can differ because lenders may adjust for daily accrual or rounding.

What APR Means in This Estimate

APR is an annualized percentage used to describe borrowing cost. It may reflect interest and certain charges, depending on the loan and the lender’s disclosure. This calculator does not separately identify or add fees: it treats the APR input as the fixed annual rate used in the payment formula. If an advertised APR incorporates charges in a way that does not match this monthly amortization model, the estimated payment may not reproduce the lender’s quoted payment.

APR is also different from the amount of interest paid over the whole loan. A percentage rate is an input; total interest is a dollar result that depends on the principal, rate, and length of repayment. A longer term can lower the scheduled monthly payment for a given principal and rate, while increasing the number of periods over which interest is charged. The calculator reports those arithmetic effects without judging a loan or making a personal recommendation.

How to Use and Read the Results

Enter the amount you expect to borrow, the APR shown in the relevant lender information, and the repayment term in years. For a term stated in months, divide the number of months by 12; for example, 48 months is 4 years. Use the APR as a percentage, such as 8 for 8%, not 0.08. The calculator accepts rates from 0.01% to 100% and terms from 0.0833 to 50 years, within its stated input limits.

• Monthly payment is the modelled amount of each regular payment toward principal and interest.
• Total interest is the total of those rounded payments minus the original loan amount.
• Total scheduled payments can be worked out as monthly payment × number of months; it includes principal as well as interest.

These outputs do not tell you the full amount due each month if the loan has separate charges, nor do they account for changes in a variable rate. To compare the calculator with a written quote, use the same principal, APR, term, payment frequency, and fee treatment. Ask the lender for the exact payment schedule and the figures used in its disclosure.

Common Sources of Differences

A calculator result may differ from a quote even when the visible APR looks the same. The lender may calculate interest using daily balances, include a financed fee in the starting balance, use a different payment date, or round each period differently. A quoted payment may also include non-loan costs that this calculator leaves out. Check whether the principal is the amount financed or merely the purchase price before entering it.

Rounding matters over many payments. This page rounds the monthly payment to cents and uses that rounded value to calculate total interest, as shown above. Some schedules calculate with extra internal precision and round only displayed amounts, or adjust the final payment to clear a small remaining balance. The displayed total is therefore a consistent estimate under the stated method, not a promise of the precise final amount charged.

Limits and Related Questions

This is a fixed-rate, fully amortizing loan calculation: the same payment is scheduled each month, and the balance is intended to reach zero after the term. It does not model an interest-only period, balloon payment, skipped payment, extra principal payments, changing rate, or refinancing. It also does not determine whether a lender will approve an application or supply a particular rate. Obtain actual rates, charges, and repayment terms directly from the lender, then use those disclosed figures as inputs.

For a loan with extra payments or a changing balance, the schedule needs additional inputs and a different calculation. Likewise, an APR that includes charges cannot be translated into a complete fee breakdown from APR alone. The formula is useful for understanding the relationship between principal, rate, and term, but it cannot replace a lender’s itemized figures.

Frequently Asked Questions

Is APR the same as the interest rate?
Not necessarily. APR is an annualized borrowing-cost measure that may account for certain charges, while an interest rate describes the rate applied to the borrowed balance. This calculator uses the entered APR as its monthly amortization rate and does not add fees separately.

Why does a longer loan term change the payment?
The same principal is spread across more monthly payments, which generally lowers the payment calculated by this formula. More payment periods also mean interest accrues for longer, so total interest can rise when the principal and rate are unchanged.

Does the monthly payment include fees or insurance?
No. The result includes modelled principal and interest only. Fees, taxes, insurance, PMI, and escrow are not inputs and are not included.

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

Why is my lender’s payment slightly different?
Possible reasons include fees added to the balance, daily rather than monthly interest calculations, payment timing, and rounding conventions. Compare the assumptions and ask the lender which principal and charges its quoted payment includes.

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

Related

• Prepayment Budget Plan Calculator and Guide
• Progressive Grace Period for Late Payments
• Peoples Gas Budget Payment Plan Explained

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