calculate-loan

01 Loan payments

Monthly Loan Repayment Calculator and Payment Formula

Calculator No. 01-0129 · 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.

A monthly loan repayment calculator estimates your fixed payment from the amount borrowed, annual interest rate (APR), and loan term. Enter those three figures to see the monthly payment and the total interest calculated over the full term.

Formula

The calculator uses the standard fixed-payment loan formula. It assumes equal payments made monthly over the stated term:

Payment = P × r ÷ [1 − (1 + r)−n]

  • P is the loan principal, in dollars.
  • r is the monthly interest rate as a decimal: APR ÷ 1,200. For an 8% APR, r = 0.08 ÷ 12.
  • n is the number of monthly payments: loan term in years × 12.

Total interest is estimated as the rounded monthly payment multiplied by the number of payments, minus the original principal: total interest = payment × n − P. The payment output is rounded to cents before total interest is calculated, so the result reflects the displayed monthly amount.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% annual APR, and a 5-year term—the monthly rate is 0.08 ÷ 12 = 0.0066667, and the number of payments is 5 × 12 = 60.

  1. Substitute into the payment formula: 20,000 × 0.0066667 ÷ [1 − (1.0066667)−60].
  2. The monthly payment is about $405.53 when rounded to the nearest cent.
  3. Total paid using that rounded payment is $405.53 × 60 = $24,331.80.
  4. Estimated total interest is $24,331.80 − $20,000 = $4,331.80.

The first result is the estimated monthly repayment: $405.53. The second is estimated interest across all 60 scheduled payments: $4,331.80.

Assumptions

  • The interest rate stays fixed for the entire loan term.
  • Payments are equal, paid monthly, and made at the end of each monthly period.
  • Interest is compounded monthly using APR ÷ 12 as the monthly rate.
  • The calculation excludes fees, taxes, insurance, PMI, escrow, and any other charges or add-ons.

When to Use a Monthly Repayment Calculator

Use this estimate to understand how principal, APR, and term combine to produce a scheduled payment. It can help you inspect a proposed loan’s arithmetic, compare hypothetical combinations of loan amount, rate, and duration, or estimate the payment before asking a lender for a formal disclosure. The calculator does not determine whether an application will be approved or whether a particular payment fits a personal budget.

Make sure the amount entered is the principal the payment formula should cover. If a lender’s quoted amount includes financed fees or other additions, the actual principal used to calculate the payment may differ from the amount you initially intended to borrow. Use the APR and term figures supplied for the specific loan when available; a sample rate is only an illustration, not a quote.

How to Read the Results

The monthly payment combines principal repayment and interest. At the beginning of 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 shrinks and more of the same scheduled payment reduces principal. The exact split depends on the loan’s rate, balance, payment timing, and contract terms.

Total interest is not the same as total cost in every situation. It is the interest implied by this formula and the rounded scheduled payment. It does not include separate charges, and it assumes every payment is made as scheduled without extra payments, missed payments, rate changes, or early payoff. A lender’s payment schedule may differ if its rounding or timing conventions differ.

Common Mistakes and Limits

  • Entering a monthly rate as APR: The rate input is annual APR expressed as a percentage. Enter 8 for 8%, not 0.08 and not 0.6667.
  • Mixing years and months: This calculator asks for the term in years and converts it to months. A five-year term means 60 scheduled payments.
  • Confusing APR with the periodic rate: The formula divides APR by 12 to get a monthly rate. Do not divide the input yourself before entering it.
  • Assuming the payment includes every housing or borrowing cost: Fees, insurance, taxes, escrow, and other charges are excluded unless included in the principal or separately modelled.
  • Rounding intermediate values too early: Small differences can result from rounding the monthly payment to cents or a lender using different calculation conventions.

This formula describes a fixed-rate, fully amortizing loan with equal monthly payments. It is not designed for a variable rate, interest-only period, balloon payment, irregular payment schedule, or a loan with a changing balance. For those cases, the contract’s payment schedule or a calculator built for those features is needed. The rate and term limits shown are calculator input limits, not statements about what any lender offers.

Frequently Asked Questions

How do I calculate a monthly loan payment?
Convert the annual APR to a monthly decimal by dividing it by 1,200, and convert years to months by multiplying by 12. Insert those values and the principal into the fixed-payment formula shown above.

Does the monthly payment include interest?
Yes. For a standard amortizing loan, each scheduled payment includes interest for that period and a portion that repays principal. This estimate excludes separate charges not entered as part of the loan amount.

Why does a longer loan term usually change the payment?
In this fixed-rate formula, a longer term spreads repayment across more monthly installments. That generally lowers the scheduled payment for the same principal and rate, while increasing the number of periods over which interest is charged.

Is APR the same as the monthly interest rate?
No. APR is entered as an annual percentage. This calculator uses APR divided by 12 as the monthly rate, expressed as a decimal, for its monthly payment calculation.

Why might a lender’s quoted payment differ?
The lender may use a different principal, rate, term, payment date, rounding method, or include charges that this calculator omits. Check the loan’s disclosure for the figures and payment schedule that apply to that offer.

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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