Loan Payment Calculator: Monthly Payment and Total Interest

This loan payment calculator estimates the fixed monthly payment and total interest for a fully amortizing loan. Enter the amount borrowed, annual percentage rate (APR), and term in years; the results show the payment and the interest paid over the scheduled term.

Formula

The calculator uses the standard fixed-payment amortization formula. It converts the annual APR to a monthly rate, calculates a payment that repays principal and interest over the selected number of months, rounds that payment to cents, and then estimates total interest using the rounded monthly payment.

• p is the amount borrowed, in dollars.
• apr is the annual percentage rate, entered as a percent, such as 8 for 8% per year.
• r is the monthly rate as a decimal: apr ÷ 1,200.
• n is the number of monthly payments: years × 12.
• pmt is the monthly payment, in dollars: p × r ÷ [1 − (1 + r)⁻ⁿ].
• int is estimated total interest, in dollars: pmt × n − p.

The payment formula assumes equal payments made monthly and a constant rate. The total-interest result uses the displayed, cent-rounded payment multiplied by the number of payments, then subtracts the original principal. Actual final payments can differ slightly because lenders may adjust the last payment for rounding or their exact accrual method.

Worked Example

Using the calculator’s default inputs—$20,000, an 8% APR, and 5 years—first convert the term to months: 5 × 12 = 60 payments. Convert APR to the monthly decimal rate: 8 ÷ 1,200 = 0.0066667.

Substitute these values into the payment formula:

Monthly payment = 20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰] = $405.53, rounded to cents.

Estimated total of scheduled payments = $405.53 × 60 = $24,331.80. Subtract the original $20,000 principal: estimated total interest = $24,331.80 − $20,000 = $4,331.80.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and begin one month after borrowing.
• Interest is modeled monthly at APR ÷ 12.
• Fees, taxes, insurance, mortgage insurance, escrow, late charges, and optional products are not included.

When to Use a Loan Payment Estimate

A payment estimate helps explain the basic relationship between principal, rate, and repayment time. It can be useful for checking a quoted payment’s arithmetic, comparing hypothetical loan amounts or terms, or seeing how much of a scheduled repayment is interest in aggregate. It does not establish whether a loan is available, suitable, or affordable for any particular person.

For a fixed rate and amount, extending the term generally reduces the required monthly payment because the balance is spread across more installments. It can also increase total interest, since interest accrues over more months. A higher APR generally increases both the payment and the interest total when the amount and term are unchanged. These are mathematical effects, not a recommendation to select a particular loan structure.

Use the APR and term that apply to the specific offer, not an estimate found elsewhere. If the lender quotes a different payment frequency, a variable rate, or a term in months, this calculator’s assumptions may not match. The lender’s documents provide the figures and payment schedule to verify.

Reading the Results and Common Mistakes

The monthly payment is the modeled amount paid each month toward principal and interest. Early in a standard amortizing schedule, more of each payment typically goes to interest; as the balance falls, more goes to principal. The total-interest figure is the modeled interest across all scheduled payments, not the total amount repaid. Add principal to interest to get the estimated scheduled repayment total.

• Entering APR as a decimal: Enter 8 for 8%, not 0.08. The calculator converts the percent to a monthly rate.
• Confusing the term units: The input is years. A five-year loan is entered as 5, and the formula converts it to 60 months.
• Leaving out financed costs: If a fee is added to the amount borrowed, the principal used for the estimate may need to include it. The calculator does not separately model fees.
• Expecting exact lender billing: Daily interest accrual, payment dates, rounding rules, and a final adjusted installment can make real statements differ by small amounts.
• Treating the estimate as an approval or budget decision: The calculation covers loan arithmetic only; it does not evaluate income, expenses, eligibility, or other obligations.

Limits and Related Loan Types

This formula is for a fully amortizing loan with one fixed APR and equal monthly payments. It is not a fit for interest-only periods, balloon payments, irregular installments, changing rates, payment holidays, or a revolving balance that can be borrowed again. A variable-rate loan can have payments or repayment timing that change when its rate changes, so a single fixed-rate estimate cannot show the full future schedule.

For a mortgage, a car loan, or a personal installment loan, the same basic calculation can estimate principal-and-interest payments if the loan meets those assumptions. The result does not include related items such as property costs, vehicle expenses, insurance, taxes, or lender charges. Student and other specialized loan arrangements may have features or program rules that are not represented by this general arithmetic; check the relevant documents or servicer for their terms.

If a loan includes an upfront fee, the APR and the amount financed may not describe the offer in the same way. Use the lender’s stated APR and principal consistently, and ask for an itemized payment schedule if the quoted figure does not match. This calculator does not calculate APR from fees or determine the balance remaining after a given number of payments.

Frequently Asked Questions

How do I calculate a monthly loan payment?
Convert annual APR to a monthly decimal rate by dividing by 1,200, convert the term to months, and apply the fixed-payment amortization formula shown above. This calculator performs those steps and rounds the payment to cents.

Does the monthly payment include interest?
Yes. The modeled payment includes both principal repayment and interest. The calculator’s total-interest output estimates the interest over all scheduled payments; it does not add that amount into the displayed monthly payment.

Why does a longer loan term change total interest?
A longer term means more monthly payment periods. Although the scheduled monthly payment may be lower for the same principal and fixed rate, interest is modeled for a longer period, which can increase the overall interest total.

Does this estimate include fees or insurance?
No. It models principal and interest only. Fees, insurance, taxes, escrow, and other charges are excluded unless they are already reflected in the amount or APR you enter; the lender can clarify how its quote treats them.

Why might the lender’s payment differ?
The lender may use different payment dates, day-count or interest-accrual methods, rounding, financed charges, or a final adjusted payment. Compare the calculator’s assumptions with the lender’s disclosed schedule.

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

Related

• Loan Payment Calculator: Estimate Monthly Payments
• Loan Payment Equation: Formula and Calculator
• Loan Payment Authorization: Meaning and Monthly Payment

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