calculate-loan

01 Loan payments

Monthly Payment Calculator: Formula and Example

Calculator No. 01-1658 · Updated · Formula and assumptions shown below

Monthly payment $405.53
Total interest
$4,331.67
= Monthly payment × loan term × 12 − loan amount
Loan amount
$20,000
Input
Interest rate (APR)
8 %
Input
You enter
Loan amount ($), Interest rate (APR) (%), Loan term (years)
You get
Monthly payment ($), Total interest ($)
Rounding
2 dp

Estimate for education, not financial advice. The result follows from the numbers you enter and the formula shown. It is not a quote or an offer, and it does not include fees, taxes or insurance unless the calculator asks for them. Ask your lender for the exact figures.

This monthly payment calculator estimates the level payment needed to repay a fixed-rate loan over a set term. Enter the loan amount, annual percentage rate (APR), and term in years; it returns the monthly payment and total interest using a standard amortization formula.

Formula

The calculator uses the fixed-payment amortization formula. The monthly payment is the loan principal multiplied by the monthly interest rate, divided by one minus the factor for discounting that payment across all monthly periods:

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. For example, 8% APR gives r = 0.08 ÷ 12.
  • n is the number of monthly payments: loan term in years × 12.

Total interest is calculated as monthly payment × n − P. Because the displayed payment is rounded to the nearest cent, the interest estimate uses that rounded payment. A lender’s final schedule may differ slightly because of its payment dates, rounding rules, or other contract details.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and a five-year term—the monthly rate is 0.08 ÷ 12 = 0.0066667, and the number of payments is 5 × 12 = 60.

Payment = 20,000 × 0.0066667 ÷ [1 − (1.0066667)−60]

The unrounded payment is about $405.528, which rounds to $405.53 per month. Total interest, using the rounded payment, is $405.53 × 60 − $20,000 = $4,331.80. The corresponding total of scheduled payments is $24,331.80.

When to Use a Monthly Payment Calculator

Use this estimate to understand how principal, APR, and repayment time combine into a regular loan payment. It can also help you compare hypothetical loan structures by changing one input at a time. For a meaningful comparison, keep the amount and term consistent and enter the APR or rate quoted for the particular loan scenario; do not treat the example defaults as a current market rate.

The result represents principal and interest only. It is not necessarily the entire amount due each month. A mortgage payment, for example, may also involve taxes, insurance, mortgage insurance, or escrow; an auto loan may have separate costs. Entering a different loan amount or APR changes the estimate, but those figures must come from your own scenario or lender disclosure.

How to Read the Results

Monthly payment is the level principal-and-interest amount implied by the inputs. Total interest is the estimated interest over the full term, calculated after rounding the payment to cents. The total of payments can be found by adding the original principal to the displayed total interest.

With the amount and APR unchanged, extending the term usually lowers each scheduled payment because repayment is spread over more months, while increasing the total interest estimate. A shorter term usually raises the monthly payment and reduces the number of interest-accruing periods. These are mathematical effects of the formula, not a statement about what term or payment is appropriate for any person.

Common Mistakes and Limits

  • Entering the wrong rate format: Type an annual APR as a percentage, such as 8 for 8%, not 0.08. The calculator converts it to a monthly decimal rate.
  • Mixing years and months: The term input is in years. A five-year term means 60 monthly payments, not five payments.
  • Confusing APR with the monthly rate: APR is not entered directly as the monthly decimal. The formula divides the annual percentage by 1,200.
  • Expecting a first bill or payoff quote: The formula assumes equal payments at regular monthly intervals. Actual billing, accrued interest, payment timing, and payoff amounts can differ.
  • Ignoring extra costs: Fees, taxes, insurance, escrow, and other charges are not inputs and are excluded from both outputs.

This calculator assumes a positive fixed APR and a level payment for every month. It does not model variable rates, interest-only periods, deferred payments, balloon payments, irregular payment dates, extra payments, or fees financed into the balance unless those amounts are included in the principal you enter. Its total-interest figure is an arithmetic estimate, not a full lender amortization schedule.

Assumptions

  • The interest rate stays fixed for the full term.
  • Payments are equal and made monthly at regular intervals.
  • Interest is compounded monthly using APR ÷ 12.
  • Fees, taxes, insurance, mortgage insurance, escrow, and other charges are not included.

Frequently Asked Questions

How do I calculate a monthly loan payment?
Convert the annual APR to a monthly decimal rate, multiply the principal by that rate, and divide by one minus (1 + the monthly rate) raised to the negative number of monthly payments. The calculator performs those steps.

Does this monthly payment include taxes and insurance?
No. It estimates principal and interest only. Taxes, insurance, escrow, mortgage insurance, and fees are not included.

Why does a longer loan term reduce the monthly payment?
The same principal is repaid across more monthly payments. The longer schedule can also increase total interest because interest accrues over more payment periods.

Why might my lender’s payment differ?
The lender may use different rounding or payment-date conventions, include charges that this calculator excludes, or calculate the payment from contract-specific terms. Check the loan disclosure for the actual figures.

Is APR the same as the monthly interest rate?
No. APR is entered as an annual percentage. This calculator divides it by 12 and converts the percentage to a decimal to obtain the monthly rate used in the formula.

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

Related

Formula used
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

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard loan formula for this calculation, fixed rate and monthly compounding unless stated, rounded as each result states. Not financial advice; no lender, rate or product is recommended. See formulas and assumptions, the disclaimer or report an error.

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