calculate-loan

01 Loan payments

Loan Payment Calculator: Monthly Payments and Interest

Calculator No. 01-5035 · Updated · Formula and assumptions shown below

Monthly payment $405.53
Total interest
$4,331.80
= 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 loan payment calculator estimates a fixed-rate loan’s monthly payment and total interest from the amount borrowed, annual percentage rate (APR), and term in years. Enter those figures to see the scheduled payment and the interest total calculated using that payment.

Formula

The calculator uses the standard fixed-payment amortizing-loan formula. It first finds the monthly payment, rounded to the nearest cent, then multiplies that rounded payment by the number of monthly payments and subtracts the original principal to estimate total interest.

Monthly payment: M = round[P × r / (1 − (1 + r)−n), 2]

Total interest: I = M × n − P

  • P is the loan principal, in dollars.
  • APR is the annual percentage rate, entered as a percentage per year.
  • r is the monthly rate as a decimal: APR ÷ 1,200.
  • n is the number of monthly payments: years × 12.
  • M is the monthly payment in dollars, rounded to cents.
  • I is estimated total interest in dollars over the full term.

The APR input must be above zero because this version of the formula uses a positive periodic rate. It accepts rates from 0.01% through 100% and terms from 0.0833 through 50 years; the actual limits of any loan depend on the lender and product. The calculator does not determine an offered rate or establish whether an applicant qualifies.

Worked Example

Using the calculator’s default inputs: P = $20,000, APR = 8%, and a term of 5 years.

  1. Convert the APR to a monthly decimal rate: r = 8 ÷ 1,200 = 0.0066666667.
  2. Find the payment count: n = 5 × 12 = 60 months.
  3. Substitute the values: M = round[20,000 × 0.0066666667 ÷ (1 − (1.0066666667)−60), 2] = $405.53 per month.
  4. Use the rounded monthly payment for the total: $405.53 × 60 = $24,331.80 in scheduled payments.
  5. Subtract principal: I = $24,331.80 − $20,000 = $4,331.80 total interest.

Because the payment is rounded to cents, the final payment on a real amortization schedule may be adjusted slightly to bring the balance to zero. The calculator’s total uses the same rounded payment for every month, as specified by its formula.

Assumptions

  • The interest rate remains fixed for the whole term.
  • There are equal monthly payments, made at the end of each monthly period.
  • Interest is compounded monthly using APR divided by 12.
  • Fees, taxes, insurance, PMI, escrow, and other charges are not included unless represented in the loan amount or APR supplied.

How to Read the Results

The monthly payment is the amount the formula assigns to principal and interest each month. Early in a typical amortizing schedule, a larger share of each payment goes to interest; as the principal falls, the interest portion generally shrinks and more of the payment reduces principal. The total-interest result is the sum implied by the fixed payment over the stated number of months, less the original amount borrowed.

A payment estimate is not necessarily the full monthly housing or borrowing cost. For example, a mortgage payment may be collected alongside property-related costs or insurance, while an auto or personal loan may have separate fees. Check which charges are included in the APR and the lender’s payment disclosure; do not add charges twice if they are already included in the figures.

When to Use This Calculation

Use this estimate to understand how principal, rate, and term relate under a fixed-rate, equal-payment structure. You can change one input at a time to see its arithmetic effect: a larger principal generally raises the payment; a higher rate raises the payment and interest total; and a longer term generally lowers the scheduled monthly payment while increasing the number of months interest can accrue.

These are mathematical comparisons, not predictions of the terms available to a particular borrower. Enter the rate and fees provided for the specific loan if you want an estimate based on an offer. If a rate can change, the calculation only describes the stated rate and does not forecast later payments.

Common Calculation Mistakes and Limits

  • Entering 8 instead of 0.08: APR is entered as a percentage, so enter 8 for 8%; the formula converts it to a monthly decimal rate.
  • Confusing the term with months: This calculator asks for years and multiplies by 12. A five-year term means 60 payments.
  • Assuming total interest is the total paid: Total interest excludes the principal. Add principal to interest to estimate all scheduled payments.
  • Ignoring rounding: The payment is rounded to cents before calculating total interest. A lender’s final payment can differ slightly because of daily interest, payment dates, or its rounding method.
  • Using it for a different payment pattern: It does not model interest-only periods, a variable rate, irregular payments, balloon payments, skipped payments, or extra principal payments.

The formula treats APR as a nominal annual rate divided into 12 equal monthly periods. Actual loan documents and servicing methods may define accrual, fees, and payment timing differently. Use the lender’s figures for exact schedules, payoff amounts, and charges.

Frequently Asked Questions

How do I calculate a monthly loan payment?
Convert APR to a monthly decimal by dividing by 1,200, convert the term to months, and use the fixed-payment formula shown above. Round the result to cents.

Does the payment include interest and principal?
Yes. For a standard amortizing loan, each scheduled payment covers interest due for that period and reduces principal, assuming the payment is made as scheduled.

Why does a longer loan term usually cost more interest?
A longer term means more payment periods during which interest can accrue. The scheduled monthly amount may be lower, but total interest can be higher under the same rate and principal.

Is APR the same as the interest rate?
Not always. APR is an annualized cost measure that may reflect certain loan charges, while the note rate is the rate used to calculate interest. How charges are treated depends on the loan disclosure, so use the relevant lender-provided figures.

Can I use this for a variable-rate loan?
Only as a snapshot using one stated rate. The calculator assumes that rate stays fixed for the full term and cannot estimate future payment changes.

Why is my lender’s payment different?
The disclosed payment may account for fees, a different rate or term, payment timing, a financed charge, or a final-payment adjustment. Compare the loan’s exact principal, APR, term, and included costs with the calculator inputs.

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 | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 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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