Amortization,
to the penny.

Field guide

How loan amortization actually works.

Amortization is the schedule by which a fixed-rate loan is paid off — each payment splits between interest on the remaining balance and principal that reduces it. Early payments are mostly interest; later ones are mostly principal. By the final payment, the entire balance is gone. This calculator generates that schedule precisely, payment by payment, for any loan amount, rate, and term.

The amortization formula

For a fixed-rate fully-amortizing loan, the constant monthly payment is given by:

where L is the loan principal, r is the per-month interest rate (the annual rate divided by 12 and by 100), and n is the total number of monthly payments. Each month then breaks apart as:

That last balance becomes next month's starting point. Plug it back in and repeat. That's the schedule.

Simple interest vs. amortization

This is the most common point of confusion for borrowers and it's critical for ranking on this topic, so it's worth being precise.

Simple interest means interest is computed once on the original principal and stays flat for the life of the loan. If you borrow $10,000 at 5% simple interest for 3 years, you pay 10,000 × 0.05 × 3 = $1,500 in interest, period. The principal is paid back separately at the end (a balloon payment) or evenly across the term. Simple interest is what you sometimes see on short personal loans, friend-to-friend lending, and some auto-title loans.

Amortization is different in two important ways:

• The interest is recomputed every month on the remaining balance, not the original principal. Because the balance shrinks each month, the dollar amount of interest also shrinks.
• The total payment is constant — a fixed number you can budget around. As interest falls each month, principal automatically rises by the same amount, so the sum stays the same.

This is why the early years of a 30-year mortgage feel like you're “not making progress”; most of each payment is interest, because the balance is still huge. By year 10–15, the balance is small enough that principal dominates and the loan accelerates toward payoff.

Worked example: $250,000 at 6.5% over 30 years

With L = $250,000, annualRate = 6.5%, n = 360 months, the monthly rate is r = 0.065 ÷ 12 ≈ 0.005417. Plugging into the amortization formula gives a monthly payment of about $1,580.17.

On payment #1, the entire $250,000 is still outstanding, so:

• Interest = 250,000 × 0.005417 ≈ $1,354.17
• Principal = 1,580.17 − 1,354.17 = $226.00
• New balance = $249,774.00

On payment #180 (halfway through), the balance is around $190,300, so interest drops to ~$1,031 and principal climbs to ~$549. By payment #360, almost the entire payment goes to principal and the loan closes out. Across all 360 payments you pay about $568,861: meaning $318,861 in interest on a $250,000 loan, or 128% of the original principal.

Why early payments are mostly interest

The math is unavoidable: when the balance is large, the interest charge that month is large in absolute terms, even at a modest rate. A balance of $250,000 at a 6.5% APR generates about $1,354 of interest in the very first month, so an $1,580 payment leaves only ~$226 to chip at principal. As principal pays down, the next month's interest is calculated on a smaller balance and the principal slice of the payment grows accordingly.

Plotting principal vs. interest over time produces a characteristic crossover curve: in the first third of a 30-year mortgage, principal stays low; in the middle third, the two lines cross; in the final third, principal dominates.

The power of an extra payment

Because every dollar of extra principal eliminates the future interest that would have accrued on it, even modest extra payments compound dramatically over a long term. A single $5,000 lump-sum payment in year one of a $250,000 / 6.5% / 30-year mortgage saves roughly $25,000 in interest and shaves about 14 months off the payoff. An extra $200 per month from day one trims roughly 7 years from the term and saves over $100,000.

The intuition: extra principal is not just “paying off faster,” it's erasing the multi-decade compounding tail on whatever amount you prepay.

Reading the schedule

The table above shows two views — Yearly (a 30-row summary that's mobile-friendly) and Monthly (the full 360-row schedule for any standard mortgage). Each row tracks:

• Principal: the share of this payment that reduces the loan balance.
• Interest: the share that goes to the lender as the cost of borrowing.
• Total interest: running total interest paid through this row.
• Balance: outstanding principal after this payment.

Common variations not modelled here

• Adjustable-rate loans (ARMs) reset the rate at fixed intervals; the schedule re-amortizes each time. This calculator assumes a fixed rate.
• Interest-only periods defer principal for the first few years; payments rise once the loan starts amortizing.
• Balloon loans amortize on a longer schedule but require the remaining balance as a lump sum at a shorter horizon.
• Negative amortization happens when the payment is set below the interest charge and the unpaid interest is added to the balance. Avoid it.

Disclaimer

This calculator computes a fixed-rate amortization schedule using the standard textbook formula. Real-world payments often include escrowed property taxes, homeowners insurance, HOA fees, and (for low down payments) PMI — for a full housing payment, use the Mortgage Calculator. For a loan that supports an extra-payment simulator, use the Loan Calculator.