Amortization Calculator

Formula

Each Payment: Interest = Balance × Rate; Principal = Payment - Interest

Interest is calculated on the remaining balance, then subtracted from the fixed payment to determine principal. The principal reduces the balance for the next calculation.

Worked Examples

Example 1: 30-Year Mortgage Amortization

Problem:Create an amortization overview for a $250,000 mortgage at 6% for 30 years.

Solution:Monthly payment calculation: P = $250,000, r = 6%/12 = 0.5%, n = 360 M = $250,000 × [0.005(1.005)^360] / [(1.005)^360 - 1] M = $1,498.88/month Payment #1: Interest = $250,000 × 0.005 = $1,250 Principal = $1,498.88 - $1,250 = $248.88 New Balance = $249,751.12 Payment #360: Interest = $7.47 Principal = $1,491.41 Final Balance = $0

Result:Payment: $1,498.88 | Total Interest: $289,595 over 30 years

Example 2: Impact of Extra Payment on 15-Year Loan

Problem:How does $200 extra monthly affect a $150,000 loan at 5.5% for 15 years?

Solution:Standard payment: $1,225.63/month With $200 extra: $1,425.63/month Without extra: - 180 payments - Total interest: $70,613 With $200 extra: - Paid off in month 144 (12.0 years) - Total interest: $55,215 Savings: - 36 months earlier (3 years) - $15,397 interest saved

Result:$200 extra saves $15,397 and 36 months

Example 3: Year 1 vs Year 30 Payment Breakdown

Problem:Compare principal vs interest in year 1 and year 30 of a $200,000 mortgage at 6.5%.

Solution:Monthly payment: $1,264.14 Year 1 (12 payments): - Principal paid: $2,235 - Interest paid: $12,934 - Principal %: 14.7% Year 30 (final 12 payments): - Principal paid: $14,649 - Interest paid: $521 - Principal %: 96.6% Note how interest drops from about 85.3% of the first-year cash flow to roughly 3.4% in the final year.

Result:Year 1: 17% principal | Year 30: 98% principal

Frequently Asked Questions

What is an amortization schedule?

An amortization schedule is a table showing each loan payment broken down into principal and interest components, along with the remaining balance after each payment. It demonstrates how the loan balance decreases over time and how the proportion of principal vs. interest changes throughout the loan term.

How does extra payment affect my amortization?

Extra payments go directly to principal, reducing your balance faster than scheduled. This means: 1) Less interest accrues on future payments, 2) More of each subsequent payment goes to principal, 3) You pay off the loan early, 4) You save significantly on total interest. Even small extra payments compound to major savings.

What's the difference between amortization and simple interest?

Simple interest is calculated only on the original principal: Interest = Principal × Rate × Time. Amortized loans calculate interest on the remaining balance, which changes with each payment. Credit cards typically use compound interest (interest on interest). Most mortgages and auto loans use amortization.

Can I get a copy of my amortization schedule?

Yes! Your lender must provide one upon request. You can also generate one using calculators like this one. Having a schedule helps you: track your payoff progress, understand your payment breakdown, plan extra payments strategically, and verify your lender's calculations.

How does refinancing affect my amortization?

Refinancing restarts your amortization schedule. If you refinance a 30-year loan after 5 years into a new 30-year loan, you're back to paying mostly interest. However, if the new rate is significantly lower or you refinance to a shorter term, you may still come out ahead. Calculate the total cost of each scenario.

What is negative amortization?

Negative amortization occurs when your payment doesn't cover the interest due, causing the unpaid interest to be added to your principal. Your balance actually grows instead of shrinking. This can happen with certain adjustable-rate mortgages or payment-option loans. It's risky and can lead to owing more than your home is worth.

How do I read an amortization table?

Key columns: Payment Number/Date, Payment Amount (usually fixed), Principal (portion reducing your debt), Interest (cost of borrowing), Total Interest (cumulative interest paid), and Balance (remaining loan amount). Watch how principal increases and interest decreases over time - this is normal amortization.

Background & Theory

An amortization schedule reveals exactly how your loan payments are applied over time. Understanding this breakdown is crucial for financial planning, comparing loan options, and making strategic extra payments. **The Amortization Formula:** M = P × [r(1+r)^n] / [(1+r)^n - 1] Where: - M = Monthly payment - P = Principal (loan amount) - r = Monthly interest rate (annual rate ÷ 12) - n = Total number of payments **How Each Payment Breaks Down:** 1. **Interest Portion:** Balance × Monthly Rate 2. **Principal Portion:** Payment - Interest 3. **New Balance:** Old Balance - Principal Paid **Why Early Payments Are Mostly Interest:** Example: $200,000 loan at 6% - Month 1 interest: $200,000 × 0.005 = $1,000 - If payment is $1,199.10, only $199.10 goes to principal - Month 2 interest: $199,800.90 × 0.005 = $999 (slightly less) This pattern continues - as balance shrinks, interest shrinks, leaving more for principal. **Key Amortization Concepts:** **Payment Number:** Which payment in the sequence (1 to n). **Payment Date:** When each payment is due. **Beginning Balance:** Loan balance before the payment. **Scheduled Payment:** The fixed amount due each period. **Principal Paid:** Amount reducing your debt this period. **Interest Paid:** Cost of borrowing for this period. **Ending Balance:** Remaining loan amount after payment. **Cumulative Interest:** Total interest paid to date. **Equity:** For mortgages, the portion of property you own (principal paid + down payment). **Amortization Strategies:** **1. Make Extra Principal Payments** - Every dollar extra reduces future interest - Specify "apply to principal" with your lender - Even small amounts compound significantly **2. Biweekly Payments** - Pay half your monthly payment every two weeks - Results in 13 full payments per year instead of 12 - Can reduce 30-year mortgage by 4-6 years **3. Round Up Payments** - Round $1,199.10 to $1,250 or $1,300 - Easy to remember and budget - Extra goes to principal automatically **4. Lump Sum Payments** - Apply bonuses, tax refunds, or windfalls to principal - One-time payments have outsized impact early in loan **5. Refinance Strategically** - Lower rate = more goes to principal - Shorter term = faster payoff (but higher payment) - Don't restart the clock without calculating benefits **Understanding Your Schedule:** - Print it or save digitally for reference - Track actual payments against schedule - Verify extra payments are applied correctly - Watch your progress as balance decreases - Celebrate milestones (50% paid, 10 years left, etc.)

History

Amortization as a financial concept evolved alongside the development of modern banking and lending. The word derives from the Old French "amortir," meaning "to kill" - referring to killing off a debt over time. Ancient lending was often simple interest or lump-sum repayment. The concept of spreading payments evenly while systematically reducing principal developed with more sophisticated commerce. Italian merchant banks in the 13th-15th centuries pioneered many lending innovations. They developed methods to calculate payment schedules that ensured both principal repayment and interest compensation. The mathematical formalization of amortization came with the development of financial mathematics. Actuaries and mathematicians in the 18th and 19th centuries refined the formulas we use today, creating standardized methods for calculating loan payments. Building societies (similar to savings and loans) emerged in 18th century Britain, offering members loans to purchase homes. These early mortgage products used amortization principles, though calculations were done by hand. The 20th century brought standardization. The Federal Housing Administration (FHA), established in 1934, promoted the long-term, fixed-rate, fully amortizing mortgage that became the American standard. Before this, many mortgages were short-term balloon loans requiring refinancing. Computer technology transformed amortization calculations. What once required actuarial tables and manual computation now takes milliseconds. This enabled more complex loan products and easier comparison shopping. Today's amortization schedules can account for variable rates, extra payments, balloon payments, and other complexities. Online calculators and spreadsheets make these calculations accessible to everyone, empowering borrowers to understand their loans fully.