calculate-loan

01 Loan payments

Monthly Payment Calculator: Formula and Example

Calculator No. 01-1667 · 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.

A monthly payment calculator estimates the fixed payment needed to repay a loan over a set term, using the loan amount and annual percentage rate (APR). Enter those figures and the term in years to see the monthly payment and estimated total interest; the calculation assumes a fixed rate and equal monthly payments.

Formula

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

Payment = P × r / (1 − (1 + r)−n)

  • P is the starting loan principal, in dollars.
  • r is the monthly interest rate as a decimal, calculated as APR ÷ 1,200 when APR is entered as a percentage per year.
  • n is the total number of monthly payments, calculated as the term in years × 12.

The calculator rounds the monthly payment to cents. Estimated total interest is the rounded monthly payment multiplied by the number of payments, minus the original principal: Total interest = payment × n − P. This means the interest estimate uses the displayed, cent-rounded payment.

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, or 0.0066667, and the number of payments is 5 × 12 = 60.

  1. Substitute the values: Payment = 20,000 × 0.0066667 ÷ (1 − (1 + 0.0066667)−60).
  2. The unrounded result is approximately $405.53, so the monthly payment rounded to cents is $405.53.
  3. Calculate interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

Under these assumptions, the estimated monthly payment is $405.53 and estimated total interest is $4,331.80. Actual payment schedules can differ if the lender uses different payment timing, rounding, or interest conventions.

Assumptions

  • The interest rate stays fixed for the full term.
  • Payments are equal, made monthly, and begin on the schedule assumed by the loan calculation.
  • Interest compounds monthly using APR ÷ 12.
  • The calculation excludes fees, taxes, insurance, private mortgage insurance, and escrow because none is entered as an input.

When to Use a Monthly Payment Estimate

This calculation is useful for understanding the principal-and-interest portion of a fully amortizing loan payment when the principal, APR, and repayment term are known. It can help you see how changing one input affects the mathematical payment—for example, a longer term generally spreads repayment across more installments, while a higher APR increases the interest charged under this formula.

Use figures that match the loan quote or disclosure as closely as possible. The principal should be the amount borrowed, not automatically the purchase price or the amount you hope to borrow. The APR should be entered as a percentage per year: enter 8 for 8%, not 0.08. The term is entered in years, so a 30-month term would be entered as 2.5 years.

If a quoted rate is variable, a single fixed-rate result cannot show how future rate changes might affect payments. Likewise, this calculator is not a complete mortgage, auto-loan, student-loan, or personal-loan cost model. It isolates standard loan-payment arithmetic rather than modelling every feature of a specific product.

How to Read the Results

The monthly payment is the level amount implied by the inputs under the assumptions above. Each payment covers interest due for that period, with the remainder reducing principal. Early in a typical amortizing schedule, interest makes up a larger share of the payment; as the balance falls, the interest portion generally shrinks and more of each payment goes toward principal.

Total interest is the estimated amount paid above the original principal over the full term. It is not the total of all payments: estimated payments in this example total $24,331.80, of which $20,000 repays principal and $4,331.80 is interest. The total can differ by a few cents from a real schedule if the lender adjusts the final payment to clear a small remaining balance.

Common Mistakes and Limits

  • Mixing up APR and a monthly rate: enter the annual APR as a percentage; the formula converts it to a monthly rate by dividing by 1,200.
  • Entering the wrong term unit: this calculator takes years, not months. A 60-month term is 5 years.
  • Assuming the result is the full bill: a mortgage payment may also involve escrowed taxes or insurance, and other loans may have fees or add-ons. Those costs are not included here.
  • Using a payment that is not fixed: changing rates, irregular payments, deferred interest, or a balloon payment require a different calculation.

Rounding also matters. The displayed payment is rounded to the nearest cent, and total interest is calculated from that rounded figure. A lender may use its own accrual and rounding conventions, so treat small differences as possible rather than assuming the estimate reproduces a statement exactly.

Frequently Asked Questions

What does a monthly payment include?
The calculator estimates principal and interest only. It does not add fees, taxes, insurance, mortgage insurance, or escrow charges.

How do I calculate a monthly loan payment by hand?
Convert APR to a monthly decimal rate by dividing the percentage by 1,200, convert the term to months, and substitute both into the fixed-payment formula shown above.

Why does a longer loan term change the payment?
A longer term means the principal is repaid over more monthly installments. The payment formula recalculates the amount for that longer schedule; total interest also depends on the rate and payment schedule.

Is APR the same as the monthly interest rate?
No. APR is entered here as an annual percentage. The calculator divides it by 12 to get a nominal monthly rate, represented as a decimal in the formula. Other APR definitions or lender-specific methods may not match this simplification.

Why does my lender’s payment differ?
The lender may include costs not modelled here or use different payment dates, compounding, rate terms, rounding, or a final-payment adjustment. Compare the calculator inputs with the lender’s written payment schedule.

This result is an estimate, and 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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