Amortization Schedule: Principal and Interest

This calculator estimates the monthly payment and total interest for a fixed-rate, fully amortizing loan from its amount, APR, and term. The schedule shows how each payment is divided between interest and principal, and how the balance falls over time.

Formula

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

M = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 1200 when APR is entered as a percentage per year.
• n is the total number of monthly payments: loan term in years × 12.
• M is the monthly payment, rounded to the nearest cent.

The calculator estimates total interest as M × n − P. This uses the rounded monthly payment, so it follows the payment amount displayed. It assumes the loan is fully repaid by the scheduled final payment and does not include fees or other charges.

Worked Example

Using the calculator’s default inputs—$20,000, an 8% APR, and a 5-year term—first convert the rate and term:

• Monthly rate: 8 ÷ 1200 = 0.0066667, or about 0.6667%.
• Number of payments: 5 × 12 = 60.

Substitute those values into the payment formula:

M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] ≈ $405.53

Total of the 60 rounded payments: $405.53 × 60 = $24,331.80. Estimated total interest is $24,331.80 − $20,000 = $4,331.80.

Assumptions

• The interest rate stays fixed throughout the term.
• Payments are equal, monthly, and made at the end of each monthly period.
• Interest is calculated monthly using APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, and other charges are not included.

How Principal and Interest Change

An amortization schedule lists each payment period and tracks how much goes to interest, how much reduces principal, and what remains owed. Interest is calculated on the outstanding balance. Early in a typical fully amortizing loan, that balance is relatively large, so a greater share of the fixed payment goes to interest. As principal is repaid, the balance declines, interest charges shrink, and more of each later payment goes to principal.

For a simple monthly schedule, the interest portion is the balance at the start of the month multiplied by the monthly rate. The principal portion is the payment minus that month’s interest. Subtract the principal portion from the starting balance to get the next balance. With the example, the first month’s interest is about $133.33 ($20,000 × 0.0066667). Of the $405.53 payment, about $272.20 reduces principal, leaving approximately $19,727.80. Actual statements can differ slightly because of payment dates, daily interest calculations, rounding, or loan-specific terms.

How to Read a Schedule

A schedule commonly includes the payment number or due date, beginning balance, payment, interest, principal, and ending balance. Check that the principal and interest portions add up to the payment, subject to rounding. The ending balance of one row should become the beginning balance of the next.

Across the whole schedule, principal paid should add up to the original amount borrowed, and interest paid should add up to the total interest, subject to any final-payment adjustment. Small discrepancies of a few cents may occur because lenders round each period’s interest and adjust the last payment. A schedule is an estimate rather than a substitute for the lender’s payment disclosures or account history.

What Can Change the Schedule

The calculation applies to a fixed-rate loan with regular payments and no changes to the balance. A variable rate can change the interest charged and may alter the payment or payoff timing, depending on the contract. Extra payments, missed or late payments, fees added to the balance, and payment-date changes can also make the actual schedule diverge from the original estimate.

Extra principal payments generally reduce the balance used to calculate later interest, but how they are credited and whether they change the required payment or shorten the term depend on the loan’s terms and servicing. Do not assume an extra amount is applied to principal automatically; check the lender’s instructions and the account’s transaction records. This calculator does not model extra payments or variable rates.

Common Calculation Mistakes

• Using the annual percentage directly as a monthly rate: For a percentage APR, divide by 1200—not 12—to convert to a monthly decimal. At 8%, the monthly decimal is 0.0066667.
• Confusing payment with principal reduction: The payment includes both interest and principal; the full payment does not reduce the balance.
• Comparing only monthly payments: A longer term can lower the scheduled payment while increasing the number of periods over which interest accrues. Compare the term and estimated total interest as well as the payment, while remembering that fees and other costs are excluded here.
• Assuming APR captures every cost: This formula uses APR as the rate input, but the displayed estimate does not separately add fees, insurance, taxes, or escrow. Confirm which amounts are included in any lender disclosure.

Frequently Asked Questions

What is principal in an amortization schedule?
Principal is the amount borrowed that remains unpaid. A payment’s principal portion reduces that balance; the interest portion is the charge calculated on the balance for the period.

Why is more of an early payment interest?
Interest is calculated on the outstanding balance. The balance is generally largest near the start of a fully amortizing loan, so the interest portion is larger then. As principal falls, the interest portion usually falls too.

Does an amortization schedule include taxes and insurance?
Not necessarily. A loan schedule usually tracks principal and interest. A payment collected by a servicer may also include escrow or other amounts, which this calculator does not estimate.

Why does my lender’s schedule differ by a few cents?
Monthly rounding, payment dates, daily rather than monthly interest calculations, and a final-payment adjustment can produce small differences. Fees or other changes to the account can create larger ones.

Does making an extra payment automatically shorten the loan?
Not always. The effect depends on how the payment is credited and the loan’s terms. Check with the servicer whether an extra amount will be applied to principal and how it affects the schedule.

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

Related

• RBA Interest Rate Calculator: See Monthly Interest
• Interest Rate Reduction Calculator and Loan Payment Effects
• Interest Rate Projections: How to Calculate Payments

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