Amortization Calculator — Payment, Total Interest & Schedule

What formula does this use?

The fixed-payment amortization formula is: \[ A = \frac{P \cdot r}{1 - (1 + r)^{-n}} \] where \(P\) is the principal, \(r\) is the periodic interest rate (APR divided by payments per year), and \(n\) is the total number of payments. When APR is 0%, the payment is \(A = P / n\).

Payments per year in this tool match your term unit: daily (365), monthly (12), or yearly (1).

Frequently Asked Questions

Do payments always match the term unit?

Yes. If you choose months, payments are monthly; years → yearly; days → daily.

Can I see the full amortization table?

Click Show Schedule. You can also Download CSV for Excel/Sheets.

Does this include fees, PMI, insurance, or taxes?

No—this is pure principal + interest (P&I). Add those separately if needed.

Is currency conversion performed?

No. The currency selector formats outputs with your preferred symbol only.

Amortization, Explained (Plain English)

Amortization is the process of spreading out a loan into a series of fixed, regular payments over time. Each payment covers both the interest charged on the outstanding balance and a portion of the principal you borrowed. In the early stages, payments are mostly interest, but as the balance shrinks, more of each payment goes toward principal—until the loan is fully paid off.

Amortization spreads a loan’s cost across equal payments. Each payment covers interest for the current period and the rest goes to principal. Over time, interest shrinks as the balance falls, and the principal portion grows—this is the hallmark of an amortizing loan.

Nominal APR vs. Periodic Rate vs. Effective Annual Rate

• APR (nominal): The annual percentage rate your lender quotes (e.g., 7%).
• Periodic rate (r): APR divided by the number of payments per year (12 for monthly, 365 for daily, 1 for yearly).
• Effective annual rate (EAR): Accounts for compounding: EAR = (1 + APR/paymentsPerYear)^{paymentsPerYear} − 1.

This tool uses the periodic nominal rate matching your chosen unit (days/months/years), which aligns with typical amortization schedules.

Why Your Payment Amount Is “Flat” but Your Interest Isn’t

The fixed payment is computed once, but the interest portion each period equals balance × periodicRate. As the balance drops, so does interest, leaving more of the payment to chip away at principal. Same payment, shifting mix.

Choosing the Right Term: Days, Months, or Years

• Shorter term → higher payment, much less total interest.
• Longer term → lower payment, but you’ll pay more interest overall.
• Daily schedules are useful for short-term or interest-sensitive comparisons.

Worked Example

Suppose a loan of $10,000 at 6% APR for 24 months (monthly payments). Periodic rate r = 0.06 / 12 = 0.005, total payments n = 24:

Payment A = P·r / (1 − (1 + r)−n) → A ≈ 10000·0.005 / (1 − 1.005−24) ≈ $443.21.

Month 1 interest ≈ $10,000 × 0.005 = $50, principal ≈ $393.21. By Month 24, interest is tiny and you finish at a zero balance.

Common Pitfalls

• Comparing loans by payment only: A longer term can look “cheaper” but cost more in total interest.
• Mismatched units: If a lender quotes monthly but you compute yearly, the numbers won’t line up. Match units.
• Ignoring fees: This tool is pure P&I. If your loan has financed fees, your real payments differ.

Optimization Tips

• Test a shorter term to see how much interest you save.
• Try a modest extra payment (e.g., +$25/month) in a separate scenario to visualize earlier payoff.
• Compare APRs from multiple lenders; a small APR drop can save a lot over long terms.

Mini Glossary

• Principal: The amount you borrowed (outstanding balance).
• Interest: The cost of borrowing each period: balance × periodicRate.
• Amortization schedule: A period-by-period breakdown of payment, interest, principal, and remaining balance.