Payment of Principal and Interest Calculator

This calculator estimates the fixed monthly payment that repays a loan’s principal and interest over a selected term. Enter the loan amount, annual percentage rate (APR), and term in years to see the monthly payment and total interest, excluding fees and other charges.

Formula

The calculator uses the standard fixed-payment amortization formula. It calculates the monthly payment that, under the assumptions below, pays down the loan balance to zero after the final scheduled payment:

PMT = round(P × r / (1 − (1 + r)−n), 2)

• PMT is the monthly principal-and-interest payment, in dollars.
• P is the starting loan principal, in dollars.
• r is the monthly interest rate, calculated as APR ÷ 1,200. APR is entered as a percentage per year.
• n is the number of monthly payments, calculated as years × 12.

The total-interest estimate is PMT × n − P. It uses the monthly payment rounded to the nearest cent, as displayed. This assumes the same payment amount each month and does not model a lender’s payment schedule or rounding practices beyond that calculation.

Worked Example

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

1. Convert the APR to a monthly decimal rate: r = 8 ÷ 1,200 = 0.0066666667, or about 0.6667% per month.
2. Convert the term to payments: n = 5 × 12 = 60 months.
3. Substitute into the payment formula: PMT = round(20,000 × 0.0066666667 ÷ [1 − (1 + 0.0066666667)−60], 2).
4. The monthly principal-and-interest payment is $405.53.
5. Total scheduled payments are $405.53 × 60 = $24,331.80. Subtracting the $20,000 principal gives estimated total interest of $4,331.80.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are made monthly, at the end of each monthly period, with the first payment one month after the loan begins.
• Interest is compounded monthly using APR divided by 12.
• The calculation excludes fees, taxes, insurance, private mortgage insurance, escrow, and any optional or extra payments.

What Principal and Interest Mean

Principal is the amount borrowed that remains to be repaid. A payment’s principal portion reduces that balance. Interest is the cost calculated on the outstanding balance under the loan’s rate and terms. “Principal and interest” generally refers to those two parts of a loan payment—not necessarily every amount a borrower may be billed.

For a fully amortizing fixed-rate loan, the scheduled payment is level, but its composition changes over time. Early in the schedule, the balance is larger, so more of each payment goes toward interest. As principal is repaid, interest for later periods is calculated on a smaller balance and a larger share of the same payment goes toward principal. The payment formula combines both portions into one amount.

For example, in the first month of the default example, approximate interest is $20,000 × 0.0066666667 = $133.33. Of a $405.53 payment, about $272.20 therefore reduces principal. Actual lender statements can differ by a few cents because of payment dates, daily-interest methods, and rounding.

How to Use the Estimate

Enter the principal amount, the APR shown in the loan information, and the repayment term in years. The APR field accepts a percentage, so enter 8 for 8%, not 0.08. The calculator returns the estimated monthly principal-and-interest amount and estimated interest across the full term.

Use the monthly payment to understand the modeled scheduled payment, and the total interest to see how the modeled cost accumulates across all installments. Total interest is not the same as total paid: total paid includes repayment of the original principal. In the example, $24,331.80 is the sum of payments, while $4,331.80 is the interest portion of that sum.

The result does not determine whether a lender will approve an application or what payment a particular contract will require. Enter the figures from the relevant loan disclosure for an estimate; consult the lender’s documents for payment dates, fees, and other contract-specific details.

Common Misunderstandings and Limits

• Confusing APR with a monthly rate: APR is entered as an annual percentage. The formula divides it by 1,200 to obtain a monthly decimal rate.
• Assuming every bill contains only principal and interest: A billed amount may include separate charges, depending on the loan and billing arrangement. This calculator has no inputs for them.
• Expecting the same result for variable rates: The formula holds the rate fixed. If a rate changes, future payment or interest calculations may change too.
• Ignoring payment timing and rounding: The estimate assumes regular monthly periods and rounds the payment to cents. Irregular dates, daily accrual, a final adjusted installment, or different rounding can affect the actual schedule.

This is a standard estimate for a fully amortizing loan with level monthly payments. It does not calculate a payoff quote, an interest-only payment, a balloon payment, or the effects of late or additional payments. To model a different structure, its terms and cash flows must be represented separately.

Frequently Asked Questions

Does a principal-and-interest payment include taxes and insurance?
No. This calculator estimates only principal and interest. Taxes, insurance, escrow, and other charges are not included.

Why does the interest portion shrink over time?
Interest is calculated on the outstanding principal. As regular payments reduce that balance, less interest accrues per period, so more of a level payment can go toward principal.

Is total interest the same as total repayment?
No. Total repayment includes the original principal plus interest. Here, total interest is estimated by subtracting principal from the sum of the rounded monthly payments.

Can I use this for a variable-rate loan?
Only as a fixed-rate illustration for the APR and term entered. It cannot predict future rate changes or recalculate installments when a lender changes the rate.

Why might my lender’s payment differ?
The contract may use different payment dates, interest accrual, rounding, fees, or other terms. Compare the estimate with the lender’s disclosed payment schedule.

The 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 | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2