Loan Repayment Calculator Formula and Example

A loan repayment calculator uses the loan amount, annual percentage rate (APR), and term to estimate the fixed monthly payment and total interest. Enter those figures below to see the payment and interest under a standard monthly-payment model.

Formula

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

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the amount borrowed, in dollars.
• r is the monthly interest rate as a decimal: annual APR ÷ 12 ÷ 100. For an 8% APR, r = 0.08 ÷ 12.
• n is the total number of monthly payments: loan term in years × 12.

The calculator rounds the monthly payment to the nearest cent. It estimates total interest as the rounded payment multiplied by the number of payments, minus the original loan amount: Total interest = payment × n − P. This convention makes the displayed payment and total internally consistent; an actual final installment may differ slightly because a lender can calculate interest and adjust the final amount using its own rounding and payment rules.

Worked Example

With a $20,000 loan, an 8% APR, and a five-year term, first convert the annual rate and term to monthly values:

• Monthly rate: 8 ÷ 1,200 = 0.0066667.
• Number of payments: 5 × 12 = 60.
• Substitute: payment = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
• Unrounded payment is about $405.53; rounded to cents, the monthly payment is $405.53.
• Total of the 60 rounded payments: $405.53 × 60 = $24,331.80.
• Estimated total interest: $24,331.80 − $20,000 = $4,331.80.

Assumptions

• The interest rate stays fixed for the entire term.
• Payments are equal, made monthly, and paid at the end of each monthly period.
• Interest is modelled monthly at APR ÷ 12, with no separate daily-interest calculation.
• Fees, taxes, insurance, private mortgage insurance, and escrow are not included.

How Loan Repayment Calculators Work

Each payment covers interest accrued since the prior payment and reduces the principal balance. Early in the schedule, the balance is relatively large, so a larger share of the payment goes to interest. As principal falls, the interest portion generally falls too, leaving more of each level payment to reduce principal. This process is called amortization.

The formula solves for a payment that brings the balance to approximately zero after n periods, assuming the same rate and payment timing throughout. A shorter term means fewer payments but generally requires a larger monthly payment for the same principal and rate. A longer term spreads repayment over more months and, under the same assumptions, increases the total interest calculated.

When to Use the Result

Use the estimate to understand the relationship between principal, APR, term, payment, and interest. It can help you check arithmetic or compare hypothetical inputs on a consistent basis. Enter the loan amount rather than the amount you hope to borrow, and use the APR and term shown in the lender’s written figures when available. Rates, fees, and loan terms are inputs; obtain the figures that apply to your own offer directly from the lender.

The monthly payment shown is the principal-and-interest payment implied by these inputs, not necessarily the complete amount due each month. For a mortgage, for example, taxes, insurance, escrow contributions, or mortgage insurance may add to the bill. For an auto or personal loan, fees or optional products may also affect the amount financed or the payment. Those costs are outside this calculator unless they are already included in the principal.

Common Errors and Formula Limits

• Using APR as the monthly rate: An annual rate of 8% is not 8% per month. Divide the percentage by 1,200 to get a monthly decimal rate.
• Mixing years and months: This calculator accepts a term in years, then multiplies by 12. If a loan document gives months, convert that term to years before entering it.
• Confusing payment with total cost: The payment is one monthly installment. Total interest is the estimated interest across the full term, not the total amount repaid.
• Ignoring fees or rate changes: The formula assumes a fixed rate and does not model upfront charges, variable rates, late payments, skipped payments, or extra principal payments.
• Expecting identical lender rounding: A lender may accrue interest daily, round each period differently, or adjust the last payment. Small differences from this estimate can therefore occur.

The formula is not suitable as-is for interest-only payments, balloon loans, irregular payment dates, or changing rates. Such loans need a model that reflects their specific payment schedule and terms.

Frequently Asked Questions

What is the formula for a monthly loan payment?
For a fixed-rate loan, use P × r ÷ [1 − (1 + r)⁻ⁿ], where P is principal, r is the monthly decimal rate, and n is the number of monthly payments.

How do I convert APR to a monthly interest rate?
For this standard estimate, divide the APR expressed as a percentage by 1,200. For example, 8% ÷ 1,200 gives a monthly decimal rate of about 0.006667.

Does the monthly payment include interest?
Yes. Each regular payment includes interest and a principal portion under the amortization model. The split between them changes over the life of the loan.

Why is my lender’s payment different?
The lender may use different rounding, daily interest accrual, fees included in the financed balance, a different first-payment date, or other contract-specific terms. Check the lender’s payment schedule and disclosure for the applicable figures.

Does this calculator include extra payments?
No. It assumes the same scheduled payment every month. Extra payments can change the balance and payoff timing, so estimating them requires a calculation that accounts for when and how much extra is paid.

This result is an estimate, and the lender’s disclosure gives the exact figures.

Related

• Beginning Balance: How to Calculate It
• How Minimum Balance Is Calculated
• Opening Balance: How to Calculate It

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