Monthly Loan Amortization Schedule: Formula and Example

A monthly loan amortization schedule shows how each fixed monthly payment is divided between interest and principal, and how the balance changes over time. Enter the loan amount, annual APR, and term to calculate an estimated monthly payment and total interest; the schedule mechanics below explain how to build each month’s row.

Formula

For a fixed-rate loan with equal monthly payments, the level-payment formula is:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the starting principal, in dollars.
• r is the monthly interest rate as a decimal: annual APR ÷ 12 ÷ 100.
• n is the number of monthly payments: term in years × 12.

The calculator’s APR input is a percentage per year, so its expression uses apr / 1200 for r. The payment is rounded to cents for display. The estimated total interest is the rounded monthly payment multiplied by the number of payments, less the original principal. A complete schedule applies the same monthly calculation repeatedly: interest for a month equals the opening balance × r; principal repaid equals the payment − interest; and closing balance equals opening balance − principal repaid.

Worked Example

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

1. Monthly rate: 8 ÷ 1,200 = 0.0066667, or about 0.66667%.
2. Number of payments: 5 × 12 = 60.
3. Monthly payment: 20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰] = $405.53, rounded to cents.
4. Total of the rounded payments: $405.53 × 60 = $24,331.80.
5. Estimated total interest: $24,331.80 − $20,000 = $4,331.80.

For the first schedule row, interest is $20,000 × 0.0066667 = approximately $133.33. The principal portion is $405.53 − $133.33 = $272.20, leaving an estimated balance of $19,727.80. In the following month, interest is calculated on that lower balance. Small differences of a cent can arise in a hand-built schedule because the displayed monthly rate and intermediate amounts are rounded; calculations generally retain more precision internally.

Assumptions

• The rate is fixed for the full term.
• Payments are equal and made monthly at the end of each monthly period.
• Interest is calculated monthly using APR divided by 12.
• The estimate excludes fees, taxes, insurance, PMI, and escrow; none are calculator inputs.

How to Read a Monthly Schedule

A typical schedule has one row per payment period. Useful columns include the payment number or date, opening balance, scheduled payment, interest, principal, and closing balance. The opening balance for the next row is the previous row’s closing balance. In the early part of a standard amortizing loan, the balance is relatively high, so more of the payment goes to interest. As principal is repaid, the interest amount generally falls and more of each unchanged payment goes to principal.

For the example, the first payment is $405.53, split approximately into $133.33 interest and $272.20 principal. The payment amount stays level under the stated assumptions, but its components change. By the final payment, most of the payment is principal. A lender’s actual schedule may show different figures because of its rounding method, payment dates, fees, or loan terms.

When to Use It and What It Does Not Show

An amortization schedule is useful for understanding the planned path of a fixed-rate installment loan: how quickly principal is reduced, how much interest is projected over the scheduled term, and what balance is associated with a particular payment period. It is also a way to check whether a quoted payment is broadly consistent with a stated principal, rate, and term, while recognizing that the quote may include items this calculator omits.

This calculator returns a payment and total interest, not a month-by-month table. To make a table, start with the original balance and repeat the monthly interest, principal, and closing-balance calculations for each of the 60 periods in the example. The last row may need a small adjustment to settle the remaining balance exactly, depending on rounding and the lender’s payment rules.

Amortization is not the same as a payment’s full cash cost. A mortgage payment, for example, may include escrow or other charges outside principal and interest. Some loans can have variable rates, irregular payment dates, interest-only periods, balloon payments, or fees financed into the balance; the level-payment formula does not model those features unless they are reflected in the inputs and assumptions. For the contract’s actual breakdown, use the lender’s payment schedule and disclosures.

Common Mistakes and Limits

• Entering APR as a decimal: enter 8 for 8%, not 0.08. The calculator converts the percentage to a monthly decimal.
• Using the wrong term units: the input is years, and the formula multiplies it by 12 to get months.
• Confusing interest with the whole payment: interest is only one portion; the remainder reduces principal under this model.
• Expecting every lender figure to match exactly: rounding, dates, fees, and contract-specific calculations can create differences.
• Treating the estimate as a payoff quote: an outstanding balance on a schedule is not necessarily the exact amount needed to pay off a loan on a particular date.

The formula assumes that the stated APR is the periodic-rate basis used for monthly calculations and that every scheduled payment is made as assumed. It does not model extra payments, missed payments, rate changes, late charges, or daily interest. If actual payment timing or loan terms differ, the schedule can diverge from the estimate.

Frequently Asked Questions

What is a monthly loan amortization schedule?
It is a period-by-period record showing each payment’s interest and principal portions and the remaining loan balance after payment.

How do you calculate monthly loan interest?
For this fixed-rate monthly model, multiply the opening balance by the monthly rate, calculated as annual APR ÷ 1,200. The principal portion is the payment minus that month’s interest.

Why does more of my payment go to interest at the beginning?
Interest is calculated on the outstanding balance. That balance is largest at the start, so the interest portion is larger; as principal falls, the interest portion usually declines.

Does this calculator include taxes, insurance, or fees?
No. It estimates principal-and-interest payments from principal, APR, and term only. Charges not entered separately are excluded.

Why might my lender’s schedule differ by a few cents?
Lenders may use different rounding conventions, payment dates, or contract calculations. Compare the assumptions and rely on the lender’s disclosed schedule for the exact figures.

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

Related

• Loan Amortization Graph: Payment and Balance Calculator
• Loan Amortization Formula in Excel: Payments and Schedule
• Loan Amortization Formula 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