Loan Amortization Interest Formula and Calculator

This calculator estimates the monthly payment and total interest for a fixed-rate, fully amortizing loan from its principal, annual APR, and term. Enter those three figures to see the level monthly payment and the interest paid over the full scheduled term.

Formula

For a fixed-rate loan repaid in equal monthly installments, the payment is calculated with the level-payment amortization formula:

M = P × r ÷ [1 − (1 + r)⁻ⁿ]

• M is the monthly payment, in dollars.
• P is the amount borrowed, or principal, in dollars.
• r is the monthly interest rate as a decimal: annual APR ÷ 12 ÷ 100.
• n is the total number of monthly payments: years × 12.

The total interest estimate is I = M × n − P, in dollars. In the calculator, the payment is rounded to the nearest cent before total interest is calculated. Actual loan schedules can differ if the lender uses different rounding, payment dates, or interest conventions.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% annual APR, and a 5-year term:

1. Convert APR to a monthly decimal rate: r = 8 ÷ 1,200 = 0.0066666667.
2. Find the number of payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: M = 20,000 × 0.0066666667 ÷ [1 − (1.0066666667)⁻⁶⁰].
4. The monthly payment is approximately $405.53, rounded to cents.
5. Total interest = $405.53 × 60 − $20,000 = $4,331.80.

The results for these defaults are a monthly payment of $405.53 and estimated total interest of $4,331.80.

Assumptions

• The interest rate is fixed for the full term.
• Payments are equal, monthly, and made at the end of each payment period.
• Interest compounds monthly at APR ÷ 12.
• The estimate excludes fees, taxes, insurance, PMI, and escrow, as well as any extra payments or late charges.

How Amortization Works

Amortization is the process of paying down a loan through scheduled installments. Each payment covers interest accrued since the previous payment and reduces principal by whatever remains. Early in the schedule, the outstanding balance is larger, so more of a level payment goes toward interest. As principal falls, the interest portion generally shrinks and the principal portion grows.

For a particular month, interest is approximately the outstanding balance at the start of that period multiplied by the monthly rate. The principal reduction is the payment minus that interest. For example, with the default figures, the first month’s interest is about $133.33 ($20,000 × 0.0066667); approximately $272.20 of the $405.53 payment reduces principal. The next month’s interest is calculated on the smaller balance.

This is why a fixed payment does not mean a fixed interest charge each month. The payment stays level under the formula, while its allocation changes. A standard amortization schedule lists each payment’s interest, principal reduction, and remaining balance.

Using the Result and Reading a Schedule

The monthly payment is the formula’s scheduled principal-and-interest amount, not necessarily the entire amount due on a real account. A mortgage bill, for example, may also include escrowed taxes or insurance; other loans may have separate charges. Check the lender’s payment breakdown and disclosure for what is actually included.

Total interest is the sum of interest implied by the calculated payment throughout the selected term. It is not the total amount repaid: estimated scheduled payments total $24,331.80 in the example, consisting of $20,000 principal and $4,331.80 interest. The figure assumes every scheduled payment is made on time and no balance-changing events occur.

To read an amortization table, look at the columns for beginning balance, payment, interest, principal, and ending balance. The ending balance for one period becomes the beginning balance for the next. Values may differ by a few cents from a lender’s table because real servicing calculations may round period by period.

Common Mistakes and Formula Limits

• Mixing APR units: The formula needs a monthly decimal rate. For an APR entered as 8, use 8 ÷ 1,200, not 8 ÷ 12 or 0.08 ÷ 12 if the calculator expects APR as a percent.
• Using years as months: Convert a term in years to months by multiplying by 12 before using it as n.
• Assuming APR always equals the note rate: APR and the rate used to accrue interest may not be identical in every loan disclosure. Use the contractual rate that applies to the payment calculation if it differs, and treat this calculator’s APR field as the annual rate input for the formula.
• Expecting exact lender totals: Cent rounding, first-payment timing, daily-interest methods, fees, and payment changes can alter the actual schedule.

The formula applies to a fixed-rate loan with regular, equal monthly payments that fully repay principal and interest by the end of the term. It does not model variable rates, interest-only periods, balloon payments, skipped or irregular installments, extra principal payments, or fees financed into the balance. At a zero interest rate, payment is simply principal divided by the number of payments; this calculator sets a small positive minimum APR because its displayed formula divides by the rate.

Frequently Asked Questions

How do you calculate monthly loan interest?
For a monthly-rate amortization schedule, multiply the balance at the start of the month by the monthly rate. The rate is the annual rate divided by 12 and expressed as a decimal; subtract that interest from the payment to find the principal reduction.

Does an amortization payment include interest?
Yes. The level payment in this formula includes both interest and principal. It does not automatically include separate charges such as taxes, insurance, or lender fees.

Why do early loan payments pay more interest?
The balance is highest near the start, so applying the monthly rate to it produces a larger interest charge. As payments reduce principal, later periods generally accrue less interest.

Does paying extra reduce total interest?
When an extra amount is applied to principal, it can reduce the balance on which future interest accrues and may shorten repayment. The result depends on when the payment is credited and the loan’s terms; this calculator does not model extra payments.

Is APR the same as the monthly interest rate?
No. APR is expressed annually. For this formula, divide the annual percentage by 12 and by 100 to get the monthly decimal rate. A disclosure may distinguish APR from the rate used to calculate scheduled interest.

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

Related

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• Loan Term Out Calculator: Estimate Months to Payoff
• Loan Term Options and Monthly 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