Amortization Calculator
Loan amortization is the process of paying off a debt through fixed periodic payments that cover both principal and interest.
- Formula explained step by step
- Worked examples with real figures
- 100% local math — nothing is uploaded
Amortization Calculator
Enter your numbers and press Calculate
How to use this amortization calculator
1. Loan amount: enter the principal you are borrowing, excluding closing costs and fees. For a home purchase, that is the price minus your down payment (a 20% down payment on a $437,500 home leaves a $350,000 loan). 2. Annual interest rate: type the nominal annual rate from your offer, not the APR. For context, 30-year fixed mortgage rates in the U.S. have hovered between 6% and 7% in recent years. 3. Term in years: 30 and 15 years are the standard mortgage terms; auto loans typically run 3 to 7 years.
You get three results instantly: the fixed monthly payment, the total paid over the life of the loan (payment × number of months), and the total interest, which is simply total paid minus principal.
A worthwhile experiment: switch a $350,000 loan at 6.5% from 30 to 15 years. The payment jumps from $2,212.24 to $3,048.88, but lifetime interest collapses from $446,406 to $198,798 — a saving of nearly a quarter of a million dollars.
The amortization formula, step by step
The fixed payment of a fully amortizing loan follows the standard annuity formula used across U.S. lending:
payment = P × r / (1 − (1 + r)^(−n))
where:
- P is the principal,
- r is the monthly rate: the annual rate divided by 12 and by 100,
- n is the total number of monthly payments (years × 12).
Total paid is then payment × n, and total interest is that figure minus the principal.
Worked example for a $350,000 mortgage at 6.5% over 30 years:
1. r = 6.5 / 100 / 12 ≈ 0.00541667 2. n = 30 × 12 = 360 payments 3. (1 + r)^(−n) = 1.00541667^(−360) ≈ 0.143025 4. Denominator: 1 − 0.143025 = 0.856975 5. Numerator: 350,000 × 0.00541667 ≈ 1,895.83 6. payment = 1,895.83 / 0.856975 ≈ $2,212.24
Total paid: $2,212.24 × 360 ≈ $796,405.71. Total interest: $796,405.71 − $350,000 = $446,405.71. In the special case of a 0% loan, the formula collapses to principal divided by months: $350,000 / 360 = $972.22.
Example scenarios with real U.S. numbers
Three scenarios that mirror common U.S. borrowing situations, all computed with the same annuity formula this tool runs:
| Principal | Annual rate | Term | Monthly payment | Total paid | Total interest |
|---|---|---|---|---|---|
| $250,000 | 5.5% | 15 years | $2,042.71 | $367,687.55 | $117,687.55 |
| $350,000 | 6.5% | 30 years | $2,212.24 | $796,405.71 | $446,405.71 |
| $500,000 | 7.0% | 30 years | $3,326.51 | $1,197,544.49 | $697,544.49 |
The middle row is the textbook 30-year fixed mortgage at recent market rates: total interest ($446,406) exceeds the original loan. Compare it with the first row — a 15-year term at a lower rate keeps the payment in a similar range while cutting interest by hundreds of thousands. And in the third row, a $500,000 jumbo-sized loan at 7% ends up costing nearly $1.2 million all-in. When you shop lenders, ask for the total interest figure, not just the monthly payment.
Common mistakes and edge cases
- Using APR instead of the note rate. The formula expects the nominal interest rate. APR bakes in closing costs and fees, so it is always higher; plugging it in overstates your payment.
- Entering a monthly rate as annual. If a lender quotes 0.54% per month, the right input here is 6.5 (annual). Typing 0.54 would produce an unrealistically low payment.
- A 0% rate. The general formula would divide by zero, so the calculator switches to the special case principal ÷ months — correct for 0% promotional financing on cars or appliances.
- Ignoring escrow. U.S. mortgage statements usually add property taxes and homeowners insurance to the payment. This tool computes principal and interest (P&I) only, so expect your actual bill to be higher.
- ARMs and refinancing. For adjustable-rate mortgages the result only holds during the fixed period; after each reset, the payment is recalculated on the remaining balance.
This calculator is provided for educational purposes only and does not constitute financial advice or a loan offer. Review actual terms with your lender or a qualified advisor before making decisions.
About this calculator
Most U.S. mortgages, auto loans, and personal loans are fully amortizing: every monthly payment is identical, but early on most of it goes to interest, while later payments chip away mainly at principal. This amortization calculator uses the standard fixed-payment (annuity) formula to show your monthly payment, the total you will hand over by the end of the term, and how much of that is pure interest. For instance, a $350,000 30-year fixed mortgage at 6.5% costs $2,212.24 a month — and a striking $446,406 in total interest, more than the amount you borrowed. Try different loan amounts, rates, and terms to see how a shorter term or a small rate cut changes the picture before you talk to a lender. This tool is for education only and is not financial advice.
Frequently asked questions
What is the difference between the interest rate and the APR?
The note rate (nominal interest rate) is the pure cost of borrowing and is what the payment formula uses. The APR adds lender fees and certain closing costs to express the true yearly cost, so it is always equal to or higher than the rate. Use the note rate to compute your payment, and the APR to compare offers between lenders on equal footing.
Why does most of my early payment go to interest?
Each month's interest is charged on the outstanding balance, which is largest at the start. On a $2,212.24 payment for $350,000 at 6.5%, the first month's interest is 350,000 × 0.00541667 ≈ $1,895.83, leaving only about $316 to reduce principal. As the balance shrinks, the interest portion of each identical payment falls and the principal portion grows — that crossover typically happens well past the midpoint of a 30-year loan.
What happens if I make extra payments on the loan?
Extra payments go straight to principal, which shrinks the balance that future interest is charged on. Even one additional payment a year on a 30-year mortgage can cut several years off the term and tens of thousands in interest. Most U.S. loans have no prepayment penalty, but check your note. This calculator does not model extra payments directly; to approximate the effect, rerun it with the reduced balance and remaining term.
Does this calculator work for mortgages, car loans, and personal loans?
Yes. Any fixed-rate, fully amortizing loan follows the same annuity math: fixed mortgages, auto loans, personal loans, and student loans on a standard repayment plan. Only the typical ranges differ — a mortgage might be 6.5% over 30 years while a used-car loan runs 8% over 5. It does not apply to credit-card revolving debt, interest-only periods, or balloon loans, which follow different repayment structures.