Loan Repayment Amount Formula and Monthly Calculator

The loan repayment amount formula calculates a fixed monthly payment from the amount borrowed, annual percentage rate (APR), and loan term. Enter those three figures to estimate the monthly payment and total interest; this calculator assumes regular monthly payments and a fixed rate.

Formula

For a fixed-rate loan with equal monthly payments, the payment formula is:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the principal, or amount borrowed, in dollars.
• r is the monthly interest rate as a decimal. With an APR entered as a percentage, r = APR ÷ 1,200. For example, 8% APR gives r = 8 ÷ 1,200.
• n is the number of monthly payments: loan term in years × 12.

The calculator displays the monthly payment rounded to cents. It estimates total interest as the rounded monthly payment multiplied by the number of payments, minus the original principal. Because the payment is rounded before this total is calculated, the total reflects the displayed payment.

Worked Example

Using the calculator’s default inputs: a $20,000 loan, 8% APR, and a 5-year term:

1. Convert the APR to a monthly decimal rate: r = 8 ÷ 1,200 = 0.0066666667.
2. Calculate the number of monthly payments: n = 5 × 12 = 60.
3. Substitute into the formula: Payment = 20,000 × 0.0066666667 ÷ [1 − (1.0066666667)⁻⁶⁰].
4. The unrounded payment is approximately $405.527; rounded to cents, the monthly payment is $405.53.
5. Total interest using the rounded payment is $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and paid at the end of each monthly period.
• Interest is calculated monthly at APR divided by 12, with no separate daily-interest adjustment.
• Fees, taxes, insurance, PMI, escrow, late charges, and payment-date variations are not included.

How the Repayment Amount Works

A level payment has two components: interest for that period and repayment of principal. Early in the schedule, the outstanding balance is larger, so more of the payment goes toward interest. As the balance declines, the interest portion generally shrinks and more of each payment reduces principal. If the scheduled payments are made as assumed, the balance is paid off at the end of the term, subject to rounding and the lender’s exact calculation method.

The formula is sometimes called the amortizing-loan payment formula. It works by setting the present value of all scheduled payments equal to the principal. A longer term spreads repayment over more months and generally lowers the calculated monthly payment for the same principal and rate, while increasing the number of periods during which interest accrues. The calculator’s total-interest figure makes that cost visible, but it is an estimate rather than a complete loan quote.

When to Use This Estimate

This calculation is useful for understanding the scheduled principal-and-interest payment on a fixed-rate loan when the amount, APR, and term are known. It can also help explain how changing one input affects the result. Enter the APR and term stated in the lender’s information; do not substitute an advertised figure if the rate or repayment period that applies to a specific offer is different. Get the actual rate, fees, and payment schedule from the lender.

For a variable-rate loan, the result only represents a period in which the assumed rate applies. If the rate changes, later payments or the payoff timeline may differ. Likewise, a loan with irregular payments, deferred interest, a balloon payment, or interest-only periods does not follow this simple level-payment schedule throughout its life.

Reading the Results and Common Mistakes

Monthly payment is the estimated amount allocated to principal and interest under the formula. It is not necessarily the complete amount due each month. A bill may include other items, and a lender may use a different payment schedule or add charges that this calculator does not model. Total interest is the estimated interest over the full term under the same assumptions; it is not the total of every possible loan cost.

• Mixing APR and monthly rates: Enter APR as a percentage, such as 8, not 0.08. The formula converts the annual percentage to a monthly decimal using APR ÷ 1,200.
• Using months as years: The term field is in years. A five-year term means 60 payments, not five payments.
• Comparing different loan amounts or terms: A payment alone does not show the total interest or other costs. Keep the assumptions clear when interpreting estimates.
• Assuming rounding is exact: Payments are rounded to cents, and real servicing systems may adjust a final payment to clear a small remaining balance.
• Leaving out loan-specific charges: Fees and other amounts can affect the amount financed or the amount due, but they are not included unless represented in the inputs.

Limits and Related Repayment Questions

The formula is not designed to calculate a changing-rate payment, a payoff quote for a particular date, the effect of extra payments, or the exact amount needed to close an account. Those calculations need additional details, such as the current balance, payment dates, rate changes, and how extra amounts are applied. For an exact schedule or payoff figure, use the lender’s disclosed terms and account information.

Frequently Asked Questions

How do I calculate a loan repayment amount?
Use P × r ÷ [1 − (1 + r)⁻ⁿ], where P is principal, r is the monthly rate as a decimal, and n is the number of monthly payments. For APR entered as a percentage, r = APR ÷ 1,200.

Is the repayment amount the same as the total loan cost?
No. The monthly payment is a periodic amount under the formula. Total interest is the interest estimate across the term, while total loan cost may also depend on fees and other charges that are not included here.

Does the formula include interest?
Yes. It calculates a level payment that covers interest and repays principal over the stated term, assuming the rate and payment schedule stay fixed.

Why can my lender’s payment be different?
The lender may use different dates, rounding, payment timing, financed fees, or other terms. The calculator also excludes charges such as insurance and taxes. Check the lender’s disclosure for the figures that apply to the loan.

Can I use this formula for a variable-rate loan?
Only as an estimate for a period with a specified rate. If the rate changes, the payment or repayment schedule may change too, so this fixed-rate calculation will not describe the whole loan.

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

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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