calculate-loan

01 Loan payments

Loan Payment Formula: Calculate Monthly Payments

Calculator No. 01-6472 · 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 payment formula calculates a fixed monthly payment from the amount borrowed, the annual percentage rate (APR), and the loan term. Enter those three figures to estimate the monthly payment and total interest; this estimate assumes equal payments and a fixed rate.

Formula

For a fixed-rate loan repaid in equal monthly installments, the payment is:

M = P × r ÷ [1 − (1 + r)−n]

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

The calculator’s first result rounds the payment to the nearest cent. Total interest is calculated as that rounded payment multiplied by the number of payments, minus the original principal. This follows the stated calculator convention; an actual lender’s final payment or account totals can differ because of payment dates, rounding, fees, or contract terms.

Worked Example

Using the calculator’s defaults: a $20,000 loan, 8% APR, and a 5-year term.

  1. Convert APR to a monthly decimal rate: r = 8 ÷ 100 ÷ 12 = 0.0066667.
  2. Convert years to monthly payments: n = 5 × 12 = 60.
  3. Substitute into the formula: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)−60].
  4. The unrounded result is about $405.5279, which rounds to a monthly payment of $405.53.
  5. Total interest using the rounded payment is $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

  • The interest rate is fixed for the full term.
  • Payments are equal, monthly, and made at the end of each payment period.
  • Interest compounds monthly at APR divided by 12.
  • The calculation excludes fees, taxes, insurance, PMI, and escrow; it also does not model extra payments or missed payments.

How the Formula Works

Each payment covers interest accumulated since the previous payment and reduces principal. Early in the schedule, the balance is larger, so more of the payment goes to interest. As the balance falls, the interest portion generally shrinks and more of each unchanged payment reduces principal. The formula sets the payment so that, under its assumptions, the balance reaches zero after the final scheduled payment.

The exponent, n, accounts for the full number of monthly periods. A longer term spreads repayment over more months and generally reduces the required monthly payment for the same principal and rate, while increasing the total amount paid in interest. A higher APR increases the payment and, over a fixed term, generally increases total interest. These are mathematical relationships, not a recommendation about borrowing.

When to Use It and How to Read the Result

Use the formula to estimate scheduled principal-and-interest payments when comparing hypothetical loan amounts, terms, or APR inputs. The monthly payment is not necessarily the whole amount due on a bill: products can include other charges, and a quoted payment may treat those items differently. Check the lender’s written disclosure for the actual payment schedule and included costs.

The APR input should be the annual percentage rate expressed as a percent, not a monthly decimal. For example, enter 8 for 8% APR; the formula converts it to a monthly rate by dividing by 1,200. Enter the term in years, and the calculator converts it to months. The displayed total interest uses the displayed monthly payment, rounded to cents.

Common Mistakes and Limits

  • Mixing rate formats: Entering 0.08 instead of 8 treats the APR as 0.08%, not 8%.
  • Using the wrong payment frequency: This formula is for monthly payments. It does not directly calculate weekly, biweekly, or annual installments.
  • Confusing APR with the periodic rate: The formula needs a monthly decimal rate, derived here from APR. Do not enter a monthly rate in the APR field.
  • Expecting total cost: Total interest is not the same as total borrowing cost if the loan also has fees or other charges.
  • Assuming every loan has level payments: Variable-rate loans, interest-only periods, balloon payments, irregular payment dates, and changing balances do not follow this simple schedule throughout.

At an APR of exactly zero, the payment is principal divided by the number of months; the displayed calculator uses a positive minimum APR because its formula divides by the monthly rate. For very small positive rates, the result approaches that zero-rate calculation.

Frequently Asked Questions

How do I calculate a monthly loan payment?
Convert APR to a monthly decimal rate, convert the term to months, and substitute the loan amount, monthly rate, and number of payments into M = P × r ÷ [1 − (1 + r)−n]. Round the resulting payment to cents.

Does the loan payment formula include interest?
Yes. The fixed payment covers both interest and principal. The formula can also estimate total interest by multiplying the rounded monthly payment by the number of payments and subtracting the original principal.

Why does a longer loan term usually lower the monthly payment?
The same principal is repaid across more installments, so the required amount per month is generally lower. However, interest accrues over more periods, so the total interest can be higher.

Is APR the same as the monthly interest rate?
No. APR is an annual rate expressed as a percentage. This calculator converts it to a monthly decimal rate by dividing the APR number by 1,200. Loan disclosures may also account for charges in ways this simplified calculation does not model.

Why might my lender’s payment differ from this estimate?
The lender may use different rounding, payment dates, fees, or loan terms, or include other amounts in the billed payment. A variable rate or nonstandard repayment schedule also changes the calculation.

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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