Monthly Loan Payment Calculator and Formula

This monthly loan payment calculator estimates the fixed payment needed to repay a loan over a set term, using the loan amount, annual percentage rate (APR), and term you enter. It also shows the total interest implied by the rounded monthly payment; the result is an estimate, not a lender quote.

Formula

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

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

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

The calculator rounds the resulting payment to the nearest cent. Total interest is then calculated as the rounded monthly payment multiplied by the number of payments, minus the original principal: Total interest = monthly payment × n − P. Because this uses a rounded, level payment, the final payment on an actual loan may be adjusted slightly to settle the remaining balance.

Worked Example

Using the calculator’s defaults: a $20,000 loan, 8% APR, and a five-year term.

1. Convert APR to a monthly decimal rate: 8 ÷ 1,200 = 0.0066667.
2. Find the number of payments: 5 × 12 = 60.
3. Substitute in the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
4. The unrounded payment is about $405.53; rounded to cents, the monthly payment is $405.53.
5. Total paid using that rounded payment is $405.53 × 60 = $24,331.80. Subtract the $20,000 principal: estimated total interest is $4,331.80.

Assumptions

• The interest rate stays fixed for the entire term.
• Payments are equal, made monthly, and occur at the end of each payment period.
• Interest accrues monthly at APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, and other charges are not included unless represented in the amount or rate you enter.

When a Monthly Payment Estimate Helps

A payment estimate helps show how principal, interest, and time interact. It can be used to understand a quoted loan structure, compare hypothetical combinations of amount, APR, and term, or see how changing one input affects the monthly amount. It does not establish whether a lender will approve an application or whether a payment fits a particular budget.

The inputs should match the figures for the loan being modelled. Use the amount that will actually be financed, rather than automatically using a purchase price: a down payment or trade-in may reduce the amount borrowed, while financed charges may increase it. Enter APR as a yearly percentage, such as 8 for 8%, not as 0.08. The calculator converts that percentage into a monthly rate internally.

For example, increasing the term generally spreads repayment over more months and lowers the calculated payment, while increasing the total interest under the same rate and amount. A higher APR generally raises both the payment and the interest total. These are mathematical effects under the stated assumptions; actual loan terms and charges must be obtained from the lender.

How to Read the Results and Their Limits

Monthly payment is the level principal-and-interest payment implied by the inputs. Total interest is the estimated amount paid above the starting principal when the rounded payment is made for every scheduled month. Neither output is necessarily the amount due on a real statement, which can reflect different payment dates, rounding, fees, or contract terms.

This formula is for a fully amortizing loan: each scheduled payment covers the period’s interest and reduces principal, so the balance is intended to reach zero at the end of the term. It does not model an interest-only period, a balloon payment, a variable rate, skipped or late payments, extra principal payments, or a changing payment schedule. For a variable-rate loan, the result represents only the rate entered, not future rate changes.

APR and the periodic interest rate are related but are not interchangeable in every loan disclosure. This calculator applies the simple monthly-rate assumption APR ÷ 12. If a lender’s quoted payment includes fees or uses another calculation convention, the figures can differ. Check the loan disclosure for the payment schedule, amount financed, rate basis, and charges that apply.

Common Input Mistakes

• Entering a decimal instead of a percentage: enter 8 for 8% APR, not 0.08.
• Using the wrong amount: the principal is the amount borrowed, which may differ from a vehicle price, home price, or requested amount.
• Mixing years and months: this calculator asks for years and converts the term to months. A five-year term means 60 payments.
• Expecting an all-in bill: the displayed amount excludes costs not included in the inputs, such as insurance, taxes, and escrow.
• Comparing unlike estimates: comparisons are meaningful only when the loan amount, APR convention, payment frequency, and included charges are understood.

Rounding also matters. The payment is rounded to cents before the total-interest calculation, so multiplying an unrounded payment by the term can produce a slightly different total. A real lender may adjust the last installment to clear a small remaining balance.

Frequently Asked Questions

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

Does the monthly payment include interest?
Yes. For the fixed-rate, fully amortizing loan model, each level payment includes interest for that month and an amount applied to principal. The calculator does not add separate fees, taxes, or insurance.

Why is my lender’s payment different?
The lender may use a different amount financed, payment date, APR convention, fee treatment, rounding method, or loan structure. Compare the calculator’s assumptions with the loan disclosure rather than assuming the difference is an error.

Does a longer loan term reduce total interest?
Not necessarily. With the same principal and APR, a longer term usually lowers each scheduled payment but increases the number of periods over which interest accrues, so the total interest is generally higher.

Can I use this for a variable-rate or interest-only loan?
Not as a complete projection. The formula assumes a fixed rate and equal payments that repay principal over the term. It does not model rate changes, interest-only periods, or balloon amounts.

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