calculate-loan

01 Loan payments

Loan Payment Estimator: Monthly Payments and Interest

Calculator No. 01-6467 · 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 loan payment estimator calculates an approximate fixed monthly payment from the amount borrowed, annual percentage rate (APR), and repayment term. Enter those three figures to see the estimated monthly payment and total interest; the calculation assumes regular monthly payments and a fixed rate.

Formula

The calculator uses the standard amortizing-loan payment formula. It divides the loan principal’s periodic interest cost by the portion of the loan balance repaid through each level payment:

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: years × 12.
  • Payment is the calculated monthly amount, in dollars.

Total interest is estimated as (monthly payment × n) − P. The payment is rounded to the nearest cent before total interest is calculated, matching the calculator’s displayed result. The formula applies when the rate is greater than zero; this estimator requires an APR of at least 0.01%.

Worked Example

With the default inputs, the principal is $20,000, the APR is 8%, and the term is 5 years.

  1. Convert the APR to a monthly decimal rate: r = 8 ÷ 1200 = 0.0066667.
  2. Convert the term to monthly payments: n = 5 × 12 = 60.
  3. Substitute into the formula: Payment = 20,000 × 0.0066667 ÷ [1 − (1.0066667)−60].
  4. Round the result to cents: the estimated monthly payment is $405.53.
  5. Calculate total interest using the displayed payment: ($405.53 × 60) − $20,000 = $4,331.80.

These are estimates derived from the stated inputs and assumptions. A lender’s payment schedule can differ if its calculation method, payment dates, or loan terms differ.

Assumptions

  • The interest rate remains fixed for the entire term.
  • Payments are equal, made monthly, and begin one month after the loan starts.
  • Interest compounds monthly at APR divided by 12.
  • The calculation excludes fees and any taxes, insurance, PMI, or escrow amounts.

When to Use a Loan Payment Estimator

Use the estimator to understand how principal, APR, and term affect a hypothetical installment loan. It can help you inspect payment scenarios before checking a lender’s formal disclosures. Enter the principal you expect to borrow—not an unrelated purchase price—and use the APR and term supplied for the specific loan offer when available.

The result is only the principal-and-interest payment under the model. A mortgage payment may also include taxes, insurance, mortgage insurance, or escrow. An auto or personal loan may have fees or other charges. Since those items are not inputs here, the displayed payment should not be treated as a complete monthly bill or as a measure of approval or affordability.

How Loan Amount, APR, and Term Affect Payments

  • Loan amount: With the rate and term held constant, borrowing more increases the payment and total interest.
  • APR: A higher APR increases the payment and generally increases total interest for the same amount and term. APR is entered as a percentage per year; the estimator converts it to a monthly rate.
  • Term: A longer term usually lowers the scheduled monthly payment for the same principal and rate, but the loan has more payment periods. This can increase total interest over the full schedule.

For instance, changing only the term can make the monthly figure look smaller without reducing the amount borrowed. Compare both the payment and total interest, and remember that extending or changing a real loan may involve terms or charges this calculator does not model.

Reading Results and Avoiding Common Errors

The monthly payment is the estimated amount due in each modeled month; total interest is the estimated interest paid across all scheduled payments. Adding the principal to total interest gives the total of modeled payments, not necessarily every cost associated with borrowing.

  • Enter APR as a percentage, such as 8 for 8%, not as 0.08. The formula handles conversion to a decimal monthly rate.
  • Enter the term in years. A five-year loan is entered as 5, not 60; the calculator converts years into months.
  • Use a consistent principal amount. If a loan’s financed balance includes an amount added to the borrowing, use the resulting balance rather than the original cash price.
  • Expect small differences if a lender rounds interest daily, uses different payment dates, or applies a different rounding method.

Limits and Other Loan Types

This estimator represents a fully amortizing loan with equal monthly payments and a fixed APR. It does not model variable-rate changes, deferred payments, interest-only periods, balloon payments, irregular payment schedules, or extra payments. A revolving credit balance also behaves differently from a fixed installment loan, so this formula may not describe its payment calculation.

Extra payments can change how quickly a balance falls and how much interest accrues, but they are not included in the displayed result. To model a particular loan accurately, use the payment schedule and terms in its disclosure, including any fees and payment-timing details. The APR and principal are inputs, not claims about current rates or offers; obtain the applicable figures from the lender.

Frequently Asked Questions

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

Does the monthly payment include interest?
Yes. Each modeled payment includes principal repayment and interest. The split changes over time: early payments generally allocate more toward interest, while later payments allocate more toward principal under a fixed-rate amortizing schedule.

Why is my lender’s payment different?
The lender may use different payment dates, rounding, fees, financed amounts, or loan terms. The estimate also excludes taxes, insurance, escrow, and other items that may appear in a real bill.

Does a longer loan term reduce total interest?
Not necessarily. A longer term often reduces the scheduled monthly payment, but it also means more payments accrue interest. Compare the total payment and interest estimates as well as the monthly amount.

Can I use this for a variable-rate loan?
Only as a hypothetical estimate at one fixed rate. It cannot predict future rate changes or recalculate a changing payment schedule.

The 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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