calculate-loan

01 Loan payments

Loan Installment Formula and Monthly Payment

Calculator No. 01-11719 · 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.

The loan installment formula calculates a fixed periodic payment from the amount borrowed, annual interest rate, and repayment term. Enter those three figures to estimate the monthly payment and total interest; the calculation assumes equal monthly payments and a fixed rate.

Formula

The standard fixed-payment installment formula is M = P × r / [1 − (1 + r)−n]. It finds the payment that pays down the balance and covers interest over a set number of equal periods.

  • M is the monthly payment, in dollars.
  • P is the starting loan principal, in dollars.
  • r is the monthly interest rate as a decimal: annual APR ÷ 12 ÷ 100.
  • n is the total number of monthly payments: loan term in years × 12.

The calculator’s APR input is a percentage per year, so it converts 8% to a monthly rate of 8 ÷ 1200, or about 0.0066667. The term is entered in years and converted to months. The formula requires a positive interest rate; a zero-interest loan uses the separate calculation P ÷ n.

Total interest is estimated as the rounded monthly payment multiplied by the number of payments, minus the original principal. Because the displayed payment is rounded to cents, the total is based on that rounded amount, as shown by the calculator.

Worked Example

Using the default inputs—$20,000 principal, 8% APR, and a five-year term:

  1. Convert the APR to a monthly decimal rate: r = 8 ÷ 1200 = 0.0066667.
  2. Convert the term to payments: n = 5 × 12 = 60.
  3. Substitute: M = 20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)−60].
  4. The monthly payment is approximately $405.53 when rounded to the nearest cent.
  5. Total of the rounded payments: $405.53 × 60 = $24,331.80. Estimated total interest is $24,331.80 − $20,000 = $4,331.80.

The payment is level in this model, but the portions going to interest and principal change over time. Early payments generally devote a larger share to interest because the outstanding balance is higher; as principal is repaid, the interest portion falls.

Assumptions

  • The interest rate is fixed for the full repayment term.
  • Payments are equal, monthly, and made at the end of each period.
  • Interest accrues monthly at APR ÷ 12, with no separate daily-interest convention modeled.
  • Fees, taxes, insurance, PMI, escrow, and other charges are not included.

When to Use the Formula

Use this calculation to understand the scheduled payment for a fully amortizing loan when you know the amount financed, fixed APR, and term. The same mathematical structure applies to many installment debts, including personal, vehicle, and home loans, but contract details can change the actual amount due.

Enter the principal actually financed, rather than an asset’s price if a down payment or trade-in reduces the amount borrowed. If a fee is added to the loan balance, include it in the principal only when it is genuinely financed. Use the APR provided for the loan and the repayment term in years. For an offer with a variable rate, a teaser period, or irregular payments, one fixed-rate calculation cannot represent every future payment.

The output is the scheduled principal-and-interest installment, not a complete household budget or a statement of eligibility. To estimate the full bill, separately check whether the lender or account includes other charges. Do not treat this arithmetic as a prediction of approval, affordability, or the final contract amount.

How to Read the Result

The monthly payment is what the formula assigns to each scheduled installment under its assumptions. Multiplying it by the number of installments gives the modeled amount paid over the term. Subtracting the original principal gives estimated interest over that schedule. This total does not mean the interest is charged evenly each month: the balance declines as payments are applied.

In the example, the first month’s approximate interest is $20,000 × 0.0066667, or $133.33. The remaining part of the $405.53 payment—about $272.20—reduces principal. Later interest is calculated on a smaller balance, so more of a level payment goes toward principal. Actual allocation and rounding may differ under a lender’s payment rules.

Common Mistakes and Limits

  • Mixing percentage and decimal rates: enter 8 for 8%, not 0.08. The calculator divides the annual percentage by 1200.
  • Using years as months: a five-year term means 60 monthly payments, not five.
  • Confusing APR with a monthly rate: APR is entered per year; the formula converts it to a monthly rate. Do not divide it by 12 yourself before entering it.
  • Assuming the payment includes every cost: the result excludes charges not represented by the inputs, such as insurance or fees.
  • Ignoring rounding and timing: payment rounding, payment dates, accrued daily interest, and a final adjustment can make a real schedule differ by cents or more.

The formula is for a fully amortizing loan with regular, equal payments and a fixed periodic rate. It does not model interest-only periods, a balloon balance, skipped payments, extra principal payments, changing rates, or penalties. For a zero-interest loan, divide principal by the number of payments; for a changing or irregular contract, use the payment schedule and terms supplied by the lender.

Frequently Asked Questions

What is the formula for a monthly loan installment?
For a fixed-rate loan, use M = P × r / [1 − (1 + r)−n], where r is the monthly rate and n is the number of monthly payments.

How do I convert APR to a monthly interest rate?
For this estimate, divide the annual APR percentage by 1200. For example, 8% APR becomes 8 ÷ 1200 = 0.0066667 per month.

Does the installment include interest?
Yes. Each modeled payment covers interest accrued for that period and repays some principal. It excludes separate fees and other charges unless included in the loan amount or otherwise modeled.

Why does the interest portion change if the payment is fixed?
Interest is calculated on the remaining balance. As principal falls, the interest due per period falls, so a larger share of the same payment reduces principal.

Can I use this formula for a zero-interest loan?
Not in this calculator, which requires APR above zero. For a truly interest-free loan with equal monthly payments, divide the principal by the number of payments.

Why might my lender’s payment differ?
The contract may use different timing, rounding, financed fees, a variable rate, or other charges. Check the lender’s payment schedule and disclosure for the figures that apply to the loan.

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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