How to Calculate Loan Payments: Formula and Example

Calculate a fixed monthly loan payment by entering the amount borrowed, annual percentage rate (APR), and term. The calculator estimates the monthly payment and total interest using a standard amortization formula; have the lender’s quoted figures ready for a more relevant estimate.

Formula

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

M = P × r ÷ [1 − (1 + r)−n]

• M is the monthly payment, in dollars.
• P is the amount borrowed, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 12 ÷ 100. The calculator expresses this as apr / 1200.
• n is the number of monthly payments: loan term in years × 12.

Total interest is estimated as M × n − P. The calculator’s outputs use the unrounded payment formula and display both results to cents. Lenders may calculate payment schedules with different rounding conventions, so small differences are possible.

Worked Example

Using the calculator’s default values—$20,000 borrowed, an 8% APR, and a 5-year term:

1. Convert the APR to a monthly decimal rate: 8 ÷ 1200 = 0.0066667.
2. Convert the term to payments: 5 × 12 = 60 monthly payments.
3. Substitute the values: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)−60].
4. The estimated monthly payment is $405.53.
5. Estimate total interest: $405.53 × 60 − $20,000 = $4,331.80.

The interest total uses the displayed, cent-rounded monthly payment multiplied by the number of payments, as specified by the calculator.

Assumptions

• The interest rate stays fixed throughout the term.
• Payments are equal, made monthly, and paid at the end of each monthly period.
• Interest compounds monthly at APR ÷ 12.
• Fees, taxes, insurance, PMI, and escrow are not included.

What You’ll Need

• Loan amount: Use the principal you expect to borrow, not the total of all scheduled payments. If the amount financed includes a fee or other charge, confirm the principal figure with the lender.
• APR: Enter the annual percentage rate provided for the loan. Do not substitute a monthly rate or type a percentage as a decimal: enter 8 for 8%, not 0.08. If you only have an interest rate and not an APR, the estimate may not reflect costs represented in the APR.
• Term: Enter the repayment period in years. For a term quoted in months, divide the number of months by 12; for example, 48 months is 4 years.

Get the actual amount, APR, and repayment term from the lender’s quote or loan disclosure. The calculator accepts positive loan amounts, APRs from 0.01% through 100%, and terms from about one month through 50 years. These are calculator limits, not statements about available loans.

Step-by-Step

1. Enter the principal. Type the dollar amount being borrowed in the Loan amount field. Check that you have not entered a requested amount when the figure you need is the amount that will actually be financed.
2. Enter the APR. Type the annual percentage rate as a percentage number. For instance, enter 8 for 8% APR. The formula converts it to a monthly rate by dividing by 1,200.
3. Enter the term. Type the number of years over which the loan is scheduled to be repaid. The calculator multiplies this by 12 to get the number of monthly payments.
4. Read the monthly payment. This is the estimated fixed payment for principal and interest. It is not necessarily the full amount due each month if other charges are collected with the payment.
5. Review total interest. This is the estimated interest over the full term, based on the scheduled payment and assuming every payment is made as calculated. It is separate from repayment of the original principal.
6. Compare the estimate with the lender’s figures. If the lender’s payment differs, verify the inputs and ask how the quoted figure accounts for payment dates, fees, or other charges. Use the lender’s disclosed payment schedule for the exact contractual figures.

Common Mistakes

• Mixing up APR and monthly rate: Enter the annual APR as a percentage. The formula handles conversion to a monthly rate; do not divide the entered value by 12 yourself.
• Using the wrong term unit: The field asks for years, not months. Entering 60 for a 60-month loan would be treated as 60 years.
• Confusing payment with total cost: The monthly principal-and-interest estimate does not automatically include fees, insurance, taxes, or other amounts.
• Assuming every loan has equal payments: This calculation is for a standard fixed-rate, amortizing loan. Variable rates, interest-only periods, balloon payments, and irregular schedules need different calculations.
• Expecting exact cents over the whole term: A displayed monthly payment is rounded. A lender’s rounding and payment schedule can cause a small difference in the final payment or total interest.

Tips

• Check the loan amount, APR, and term against the same written quote; figures from different offers or scenarios will not produce a meaningful match.
• When checking your own calculation, convert APR to a decimal monthly rate and years to months before applying the formula. Keep extra precision during the calculation and round the payment only for display.
• Use the total-interest result to understand the interest implied by the entered assumptions, not as a complete measure of all borrowing costs.
• If the lender gives a payment amount that includes additional charges, ask for the principal-and-interest portion and the itemized amounts so you can compare like with like.

Troubleshooting

The calculator rejects a value: Check that the loan amount is positive, the APR is between 0.01 and 100, and the term is between 0.0833 and 50 years. Convert months to years before entering the term.

The payment seems much too high or low: Recheck whether the amount is in dollars, whether APR was entered as a percentage number, and whether the term is in years. A short term generally produces fewer payments and a higher monthly payment than a longer term for the same principal and APR.

Your result does not match a lender’s quote: Confirm whether the lender is showing principal and interest alone, whether the quoted principal includes financed costs, and whether its payment dates and rounding differ from the calculator’s assumptions. Ask the lender for an itemized schedule rather than changing inputs just to force a match.

The loan has a changing rate or unusual structure: This fixed-rate formula cannot represent future rate changes, skipped or irregular payments, a balloon balance, or extra payments. Request a schedule that models the actual loan terms.

Frequently Asked Questions

How do I calculate a loan payment by hand?
Convert APR to a monthly decimal rate, convert the term to months, then apply M = P × r ÷ [1 − (1 + r)−n]. Use a calculator with adequate precision and round the payment to cents.

Does this calculator show the full monthly amount due?
No. It estimates principal and interest for a standard amortizing loan. Costs such as insurance, taxes, escrow, and fees are not included.

Why does a longer loan term usually change the payment and interest?
A longer term spreads principal repayment across more monthly payments. With a positive fixed rate, that generally lowers each scheduled payment while increasing the total interest implied by the schedule.

Can I use this for a variable-rate loan?
Only as a snapshot under the APR entered. It assumes that rate remains fixed; it does not predict future rate changes or recalculate later payments.

Does the result include extra payments?
No. The calculation assumes the scheduled equal monthly payment only. Extra payments can change the balance and payoff timing, which require a separate schedule.

Why can my lender’s payment differ by a few cents?
Rounding methods, payment timing, and the exact terms used in the lender’s schedule can create small differences. Check the disclosed amortization schedule for the figures that apply to the loan.

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

Related

• EMI Calculator: How the Monthly Instalment of a Loan Is Calculated
• Loan Calculator With Down Payment: Payment on What You Borrow
• Loan Payment Calculator: Monthly Payment, Total Interest and Cost

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