calculate-loan

01 Loan payments

Loan Repayment Calculator: Monthly Payments and Interest

Calculator No. 01-6535 · 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.

A loan repayment calculator estimates your monthly payment and total interest from the amount borrowed, annual percentage rate (APR), and loan term. Enter those figures to see the level monthly payment and the interest paid over the full term, assuming the loan stays on schedule.

Formula

The calculator uses the standard fixed-payment loan formula. It converts the APR to a monthly rate, then calculates the payment that repays principal and interest in equal installments:

  • r = APR / 1200, the monthly interest rate as a decimal.
  • n = years × 12, the number of monthly payments.
  • Payment = round(P × r / (1 − (1 + r)−n), 2).
  • Total interest = payment × n − P, using the displayed payment rounded to cents.

Here, P is the loan principal in dollars, APR is the annual percentage rate entered as a percentage, r is the monthly rate, and n is the payment count. The payment formula assumes a positive rate, which is why the APR input starts above zero.

Worked Example

Using the calculator’s defaults: principal P = $20,000, APR = 8%, and term = 5 years.

  1. Convert the APR to a monthly rate: r = 8 / 1200 = 0.0066667.
  2. Convert the term to monthly payments: n = 5 × 12 = 60.
  3. Substitute into the payment formula: $20,000 × 0.0066667 / (1 − (1.0066667)−60).
  4. Round the monthly payment to cents: $405.53.
  5. Calculate interest using that rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

The estimate is therefore a monthly payment of $405.53 and total interest of $4,331.80. Multiplying the rounded payment by the number of payments matters: calculating with an unrounded payment could produce a slightly different displayed total.

Assumptions

  • The interest rate is fixed for the entire term.
  • Payments are equal monthly installments, made at the end of each monthly period.
  • Interest compounds monthly at APR divided by 12.
  • The estimate excludes fees, taxes, insurance, PMI, and escrow. It also assumes no missed, late, or extra payments.

How to Read a Repayment Estimate

The monthly payment combines principal repayment and interest. Early in a typical amortizing loan, the outstanding balance is larger, so more of each payment goes toward interest. As the balance falls, the interest portion generally declines and more of each fixed payment reduces principal. The precise allocation for a particular payment depends on the lender’s schedule and account terms.

Total interest is the sum of the scheduled payments minus the original principal under this calculation. It is not the total amount paid: total scheduled payments are the principal plus the interest shown. In the example, that is $24,331.80 across 60 payments.

Changing the loan amount, APR, or term changes the estimate. A longer term often spreads repayment over more installments; because interest continues to accrue while a balance remains, the total interest can increase even if the monthly payment decreases. A different APR also changes both the payment and total interest. These are mathematical effects of the inputs, not a recommendation about which term or borrowing arrangement to choose.

When This Calculator Helps—and Its Limits

Use the estimate to understand the basic scheduled payment for a fixed-rate installment loan, or to compare arithmetic scenarios by entering different principal amounts, rates, or terms. Enter the loan’s principal rather than the total of all scheduled payments. Check whether the rate you have is an APR expressed as a percentage per year; do not enter a monthly rate as if it were an APR.

The calculator does not determine a lender’s actual payment schedule. A variable rate can change future payments or the payoff timeline. Fees added to a balance, a payment due date that differs from the model, irregular installments, interest-only periods, deferred payments, and extra principal payments are not represented. APR may also reflect costs that this simplified formula does not itemize, so the estimate cannot show how each charge is collected.

For an exact account figure, check the lender’s payment schedule or disclosure. Use the stated principal, rate, term, and payment frequency, and confirm whether charges are financed or billed separately. If the loan permits extra payments, the timing and instructions for applying them to principal can affect the actual balance and interest; this calculator does not model those changes.

Common Repayment Calculation Mistakes

  • Confusing APR and the monthly rate: the formula divides annual APR by 12 and by 100, hence APR / 1200.
  • Entering years as months: the input is in years; the calculator multiplies it by 12.
  • Using the amount financed instead of principal without checking: a fee financed into the loan may make the repayment principal higher than the cash received.
  • Assuming total interest includes principal: it does not; principal plus interest gives total scheduled payments.
  • Expecting exact statement figures: rounding, payment dates, fees, and contract-specific methods can create differences.

Frequently Asked Questions

How do I calculate a monthly loan repayment?
Convert APR to a monthly decimal rate by dividing it by 1200, convert years to months, and apply the fixed-payment formula shown above. Round the payment to cents.

Does a loan payment include interest?
For a standard amortizing loan, each scheduled payment includes interest and principal. The interest share usually changes over time as the outstanding balance changes.

Why does the calculator’s result differ from my lender’s payment?
The lender may use different payment dates, rounding, financed charges, a different payment frequency, or terms not included in this estimate. Compare the calculator’s inputs with the lender’s schedule.

Does a longer loan term reduce total interest?
Not necessarily. A longer term may lower each scheduled payment while allowing interest to accrue over more periods. The result depends on the principal, APR, and repayment structure.

Are extra payments included?
No. The estimate assumes only the same scheduled monthly payment throughout the term. Extra payments can change the payoff time and interest, depending on how they are applied.

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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