Loan Payment Calculator: Estimate Monthly Payments

This calculator estimates the fixed monthly payment on a loan when you enter the loan amount, annual percentage rate (APR), and term in years. It also estimates total interest over the full term, using a standard fixed-payment formula.

Formula

The monthly payment is the amount that, when paid at the end of each month, covers the month’s interest and repays the loan balance in equal installments over the selected term. The formula is:

Payment = P × r ÷ [1 − (1 + r)−n]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: annual APR divided by 12, then divided by 100. With an APR entered as a percentage, this is APR ÷ 1200.
• n is the number of monthly payments: the term in years multiplied by 12.

Total interest is calculated as monthly payment × n − P. It uses the displayed payment rounded to cents, as a real payment amount ordinarily must be stated in currency units. Actual loan schedules can differ slightly if the final payment is adjusted for rounding or the lender uses different timing or calculation conventions.

Worked Example

Using the calculator’s defaults: principal P = $20,000, APR 8%, and term 5 years.

1. Convert APR to a monthly decimal rate: r = 8 ÷ 1200 = 0.0066666667.
2. Convert the term to payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: $20,000 × 0.0066666667 ÷ [1 − (1.0066666667)−60].
4. The monthly payment rounds to $405.53.
5. Total interest using that rounded payment is $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

• The APR is fixed for the entire repayment term.
• Payments are equal, made monthly at the end of each period, with the first payment one month after the loan begins.
• Interest compounds monthly at APR divided by 12.
• The calculation excludes fees, taxes, insurance, PMI, escrow, late charges, and any optional products because they are not inputs.

When to Use a Monthly Payment Estimate

Use this estimate to understand the payment implied by a particular principal, APR, and term, or to compare hypothetical combinations by entering different values. For example, a longer term reduces the amount of principal paid in each installment, while interest continues to accrue for more months. That can lower the calculated monthly payment while raising total interest, all else equal.

The calculation is useful for the loan portion of a payment, not necessarily the full amount due each month. A mortgage bill, for example, may include taxes, insurance, or other items that are outside this formula. An auto or personal loan may also have fees or add-ons not reflected in the principal entered here. If a charge is financed into the loan, it affects this estimate only when included in the loan amount.

How to Read the Results

The first result is the estimated payment every month. The second is the sum of those rounded payments minus the original principal, representing estimated interest across the full schedule. It is not the total cash outlay: the principal is also repaid, so total payments equal principal plus the displayed interest in this model.

These outputs describe the scheduled loan only. They do not show how much interest has accrued on a particular date, the payoff amount after some payments, or the effect of making extra payments. Those questions require additional information such as payment history, payoff date, and the lender’s balance calculation.

Inputs, Limits, and Common Mistakes

• Enter APR as a percentage. Type 8 for 8%, not 0.08. The calculator converts it to a monthly decimal rate.
• Use years for the term. A five-year term means 60 monthly payments. Do not enter 60 in the years field.
• Use the amount actually borrowed. If fees or other costs are financed, include them in principal only if they are part of the stated loan amount.
• Do not treat rounded estimates as a lender quote. The payment is rounded to cents; repeated rounding and a lender’s exact daily or periodic accrual method can change the schedule slightly.

The calculator accepts APR values from 0.01% through 100% and terms from approximately one month through 50 years. The minimum APR is above zero because the displayed formula divides by the monthly rate. A zero-interest loan needs a separate calculation: principal divided by the number of payments. The formula also assumes the rate and payment schedule do not change. It cannot model variable rates, irregular payment dates, balloon payments, deferment, skipped payments, or fees paid separately.

Frequently Asked Questions

Does the monthly payment include interest?
Yes. Each level payment includes interest for that month and a portion of principal. Early payments generally contain a larger interest share than later payments under a fixed-rate amortizing schedule.

Why can a longer term lower the payment but increase total interest?
It spreads principal repayment over more installments. Because the balance remains outstanding for longer, more interest can accrue over the full schedule, assuming the same principal and APR.

Is APR the same as the interest rate?
Not necessarily. APR is an annualized rate disclosed for borrowing costs, while the contract’s interest calculation and included charges can affect how a lender’s figures relate to this simplified estimate. Use the actual APR and payment details supplied for the loan.

Why does a lender’s payment differ from this result?
Possible reasons include fees included in the loan, a different amount financed, a variable rate, payment timing, day-count conventions, or rounding. Check the lender’s payment schedule and disclosure for the figures applicable to the loan.

Does this estimate include a down payment or extra payments?
No. A down payment matters only insofar as it reduces the principal entered. Extra payments are not included; they can alter the balance and repayment schedule, so this fixed-payment result does not calculate their effect.

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

Related

• Prepayment Amortization Schedule Excel Calculator
• Principal Payment Amortization Schedule Calculator
• Prepayment Amortization Calculator: Extra Loan Payments

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