calculate-loan

01 Loan payments

Loan Repayment Calculator: Estimate Your Monthly Payment

Calculator No. 01-6532 · 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 repayment calculator estimates the fixed monthly payment needed to repay a loan, plus the total interest over the stated term. Enter the loan amount, annual percentage rate (APR), and term in years to see an estimate based on equal monthly payments.

Formula

The calculator uses the standard fixed-payment amortization formula. First, it converts the annual APR to a monthly rate and the term to a number of monthly payments:

  • r = APR ÷ 1,200, the monthly interest rate expressed as a decimal.
  • n = years × 12, the number of monthly payments.
  • p = starting loan principal, in dollars.
  • Monthly payment = round[p × r ÷ (1 − (1 + r)−n), 2].
  • Total interest = rounded monthly payment × n − p.

The payment formula spreads repayment across equal monthly installments. Each payment covers the interest accrued for that period and reduces some principal. The exact split changes over time: with a fully amortizing loan, the interest portion generally falls as the outstanding balance is paid down.

Worked Example

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

  1. Monthly rate: 8 ÷ 1,200 = 0.0066667.
  2. Number of payments: 5 × 12 = 60.
  3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)−60].
  4. Rounded monthly payment: $405.53.
  5. Total interest, using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

The total of the 60 estimated payments is $24,331.80: $20,000 repays principal and $4,331.80 is estimated interest. Actual lender figures can differ because of payment dates, rounding conventions, fees, or loan terms not represented here.

Assumptions

  • The interest rate stays fixed for the entire term.
  • Payments are equal, made monthly, and begin after one monthly interest period.
  • Interest is compounded monthly using APR divided by 12.
  • Fees, taxes, insurance, PMI, escrow, late charges, and other costs are not included.

When to Use a Loan Repayment Estimate

This estimate is useful for understanding the payment implied by a stated principal, APR, and term. It can also help illustrate how changing an input changes the arithmetic. For example, a longer term spreads principal repayment across more months; holding other assumptions constant, that generally lowers the scheduled monthly payment but increases the time during which interest accrues. A different APR also changes the result, so enter the rate supplied in the relevant lender disclosure rather than assuming the example rate applies to you.

The result is a principal-and-interest estimate, not a full monthly housing or borrowing cost. A mortgage payment may also involve property-related expenses or escrow items, while an auto or personal loan may have origination charges or other costs. Those amounts are not calculated here. If a loan uses a variable rate, irregular installments, a balloon payment, an introductory rate, or a different payment schedule, this fixed monthly formula may not describe its repayment accurately.

How to Read the Results

Monthly payment is the estimated amount for each scheduled installment under the assumptions above. It is not a statement of what a lender will charge or approve. Total interest is calculated as the rounded installment multiplied by the number of payments, less the original principal. Since the displayed installment is rounded to cents, the implied total may differ slightly from a lender’s calculation, especially if the lender adjusts the final payment.

The calculator’s term input is in years, not months. For instance, enter 5 for a five-year term; the formula converts that to 60 monthly payments. APR is entered as a percentage, so enter 8 for 8%, not 0.08. The calculator accepts a positive APR because the payment formula divides by the monthly rate. It therefore does not model a zero-interest loan.

Common Calculation Mistakes and Limits

  • Mixing annual and monthly rates: The APR must be divided by 12 and converted from percent to decimal, which is why the formula uses APR ÷ 1,200.
  • Using the wrong term unit: This calculator asks for years; entering 60 to mean 60 months would instead represent 60 years.
  • Confusing payment with total cost: The monthly result excludes charges and expenses that are not entered. Review the lender’s itemized disclosures for those figures.
  • Assuming every loan has equal payments: Interest-only periods, adjustable rates, skipped-payment arrangements, and balloon balances require different calculations.
  • Overinterpreting rounded figures: The estimate rounds the payment to the nearest cent before calculating total interest. The lender may use its own day-count, payment-date, and rounding methods.

A longer repayment term is not automatically cheaper because it may involve more interest over time, even when its scheduled installment is lower. Conversely, this calculator does not estimate the effect of extra payments. To model those, the payment schedule and the timing and treatment of additional principal must be known.

Frequently Asked Questions

How do I calculate a loan repayment?
For equal monthly payments on a fixed-rate loan, convert APR to a monthly decimal rate, convert years to months, and use the amortization payment formula shown above. Multiply the rounded payment by the number of payments and subtract principal to estimate total interest.

Does the monthly payment include interest?
Yes. The estimated installment includes both principal repayment and interest. It does not include fees, insurance, taxes, or other costs unless they are separately included in the loan payment by the lender.

Why can my lender’s payment differ from this estimate?
The calculator assumes a fixed rate, monthly compounding, equal payments, and a simple monthly schedule. A lender may account for fees, payment dates, rounding, rate changes, or other contract details that are not inputs here.

Can I use this calculator for a zero-interest loan?
No. The displayed formula divides by the monthly rate, and the APR input has a minimum of 0.01%. For a genuinely interest-free loan with equal installments, the basic arithmetic is principal divided by the number of payments, but check the contract for other charges or conditions.

Does a longer term always reduce the total repayment?
No. A longer term means more scheduled payments. It may reduce the amount due each month while increasing total interest, depending on the rate and loan terms.

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 | $ | 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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