Monthly Interest Payment Formula: How It Works

The monthly interest payment formula depends on what you mean by “interest payment.” For a simple interest-only balance, it is principal × annual rate ÷ 12; for a loan with a level monthly payment that includes principal and interest, the payment uses an amortization formula. This calculator estimates the level monthly payment and total interest from the loan amount, APR, and term.

Formula

For a fixed-rate loan repaid in equal monthly installments, the unrounded payment is:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the starting principal, in dollars.
• r is the monthly interest rate as a decimal, calculated here as APR ÷ 1,200. APR is entered as a percentage per year; dividing by 100 converts it to a decimal and by 12 converts the annual rate to a monthly rate.
• n is the number of monthly payments, calculated as loan term in years × 12.

The calculator rounds the resulting payment to the nearest cent. Total interest is calculated as the rounded monthly payment multiplied by the number of payments, minus the original principal: Total interest = payment × n − P. The total therefore reflects the calculator’s displayed payment rather than an unrounded installment.

Worked Example

Using the default inputs—$20,000 principal, 8% APR, and a 5-year term—the monthly rate is 0.08 ÷ 12 = 0.0066667, and the number of payments is 5 × 12 = 60.

1. Substitute the values into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
2. The payment before cent rounding is approximately $405.527; rounded to the nearest cent, the monthly payment is $405.53.
3. Using that rounded payment, total interest is $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are made monthly, at the end of each monthly period.
• Interest is compounded monthly using APR ÷ 12 as the periodic rate.
• The estimate excludes fees, taxes, insurance, PMI, escrow, and other charges because they are not inputs to this calculator.

How the Formula Is Derived

The formula comes from the way each payment changes the loan balance. At the end of a month, the balance grows by the monthly rate, then the payment is subtracted. If the payment is M and the starting balance is P, the balance after one payment is P(1 + r) − M. After a second month it is [P(1 + r) − M](1 + r) − M.

Continuing this pattern for n months gives a balance of P(1 + r)ⁿ − M[(1 + r)ⁿ − 1] ÷ r. A fully repaid loan has a zero balance after the final payment. Set that expression equal to zero and solve for M: M = P × r ÷ [1 − (1 + r)⁻ⁿ]. The formula spreads repayment of the principal and interest across the scheduled installments.

Interest-Only Amounts and Amortizing Payments

The phrase “monthly interest payment” can also mean the interest portion due for one month, not the whole loan installment. For a balance that does not change during the month, that amount is commonly calculated as balance × monthly rate. At $20,000 and 8% APR, the first month’s interest under the calculator’s monthly-rate assumption is about $133.33: $20,000 × 0.08 ÷ 12.

That $133.33 is not the same as the full scheduled installment. In the worked example, the $405.53 payment includes interest and principal; the remainder after the first month’s interest—about $272.20—reduces the balance. As the balance declines, the interest portion generally declines too, while a level payment remains the same, subject to rounding and the stated assumptions.

For a true interest-only arrangement, the principal is not reduced by the interest payment itself. The formula for a changing balance, daily interest accrual, or a payment schedule with variable rates may differ. Check the loan’s payment schedule or disclosure for the method and timing actually used.

When to Use It and How to Read the Results

Use the amortizing formula to estimate a fixed monthly installment when the principal, annual rate, and repayment term are known and payments are level. It can also help explain how extending the term affects the arithmetic: with other inputs unchanged, more payments spread principal repayment over more months, so each scheduled payment is generally smaller, while interest accumulates for a longer period.

The calculator’s APR field is an input, not a prediction of what any lender will offer. Enter the rate and term shown in the relevant loan information to estimate the formula-based payment. Obtain the actual rate, charges, payment dates, and repayment details from the lender’s disclosure; this page does not determine eligibility or total borrowing costs.

The total-interest output is an arithmetic estimate for the modeled payment schedule. It is not necessarily the same as a disclosed finance charge or total cost when a loan includes fees, an irregular first period, changing rates, or other charges. Small differences can also arise from how an actual servicer rounds interest and adjusts a final payment.

Common Mistakes and Formula Limits

• Mixing up percentage and decimal rates: for an APR entered as 8, the monthly decimal rate is 8 ÷ 1,200, not 8 ÷ 12 and not 0.08 ÷ 12 after also dividing by 100 again.
• Using years as payment count: a five-year monthly loan has 60 scheduled payments, not five.
• Calling the installment “monthly interest”: an amortizing installment contains principal as well as interest; the interest-only amount is a different calculation.
• Expecting exact statement amounts: payment dates, daily accrual, rounding rules, fees, and rate changes can alter real account figures.

This formula assumes a fixed periodic rate, equal payments, monthly periods, and a loan that is fully repaid at the end of the stated term. It does not model extra payments, skipped or late payments, balloon balances, variable rates, or irregular payment intervals. Those situations need their own schedule and inputs.

Frequently Asked Questions

How do I calculate monthly interest on a loan?
For a simple monthly estimate on a balance that remains unchanged for the period, multiply the balance by the annual decimal rate divided by 12. For an APR entered as a percentage, the monthly rate is APR ÷ 1,200.

Is monthly interest the same as a monthly loan payment?
No. Monthly interest is the charge for borrowing during a period. A standard amortizing payment usually covers that interest and repays part of the principal.

Why does the interest portion change each month?
With a level-payment amortizing loan, each payment reduces the balance. Interest is then calculated on the remaining balance under the loan’s accrual method, so the interest portion usually decreases as principal is paid down.

Does APR divided by 12 always match a lender’s calculation?
No. It is the monthly-rate assumption used by this estimate. A contract may specify a different accrual method, compounding convention, or timing, so consult the lender’s disclosure for the applicable calculation.

Why might my statement differ from this estimate?
Possible reasons include fees, daily interest accrual, payment timing, rounding, a variable rate, or an irregular first or final period. The calculator models only the assumptions listed above.

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

Related

• First Interest-Bearing Account: How It Works
• First Fidelity Loan Payment Calculator
• First Financial Quick Payment Calculator

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