Loan Amortization Calculator

The monthly payment on a fixed-rate amortizing loan is calculated using the annuity formula:

M = P × [r(1 + r)ⁿ] / [(1 + r)ⁿ − 1]

Where:

• M = Monthly payment (principal + interest)
• P = Loan principal (the amount borrowed)
• r = Monthly interest rate (annual rate divided by 12)
• n = Total number of monthly payments (loan term in years multiplied by 12)

Why it works: This formula ensures that if you make exactly the same payment every month for the entire loan term, you'll pay off the full principal and all accumulated interest by the final payment. It's derived from the present value of an annuity — the same concept used in bond pricing and DCF valuation.

Important notes:

• This formula applies to fixed-rate loans. Adjustable-rate mortgages (ARMs) recalculate the payment when the rate changes.
• The formula covers only principal and interest (P&I). Your actual mortgage payment may also include property taxes, homeowner's insurance, and PMI.
• Even a small rate change has a big impact. Going from 6% to 7% on a $400,000 loan increases the monthly payment by about $266 and adds over $95,000 in total interest.

Extra payments — whether monthly or annual — go directly toward reducing the principal balance. Since interest is calculated on the remaining balance, every dollar of extra principal paid today eliminates future interest charges on that dollar for the rest of the loan.

The compounding effect works in reverse: When you borrow money, the bank earns compound interest on your balance. By paying extra principal, you're effectively "uncompounding" that interest. The earlier you make extra payments, the more powerful the effect, because you're eliminating interest that would have accrued for years or decades.

Types of extra payments:

• Extra monthly payment — Adding a fixed amount to every monthly payment. Even $100 extra per month on a 30-year mortgage can shave years off and save tens of thousands in interest.
• Annual lump sum — Making one large extra payment per year (for example, using a tax refund or bonus). This is applied once per year to reduce the balance.
• Biweekly payments — Paying half your monthly payment every two weeks results in 26 half-payments (13 full payments) per year instead of 12, effectively adding one extra payment per year.

Real example: On a $300,000 loan at 7% for 30 years, your monthly payment is $1,996. Paying an extra $200/month cuts the loan from 30 years to about 22 years and saves over $100,000 in interest. That's the power of attacking principal early.

One caveat: Before making extra mortgage payments, compare the interest rate on your loan to expected investment returns. If your mortgage rate is 3% but the market averages 8-10%, you might be better off investing the extra cash. Our Debt Payoff vs. Invest calculator can help with that decision.

The interest-to-principal ratio describes what fraction of each payment goes toward interest versus actually reducing your loan balance. This ratio starts heavily skewed toward interest and gradually shifts toward principal over the life of the loan.

How it works: Each month, interest is calculated as the remaining balance multiplied by the monthly interest rate. The rest of your fixed payment goes to principal. As the balance decreases, the interest charge shrinks, leaving more room for principal repayment.

Typical progression on a 30-year mortgage at 7%:

• Year 1 — About 85-90% of each payment is interest. You're barely touching the principal.
• Year 10 — Around 75% interest, 25% principal. Still mostly interest.
• Year 20 — Roughly 50/50. The crossover point where principal starts exceeding interest.
• Year 30 — Nearly 100% principal. The last few payments are almost entirely reducing the balance.

Why this matters: If you sell your home or refinance in the first 5-10 years, you've paid a lot of interest but built relatively little equity. Understanding this dynamic helps you make smarter decisions about when to refinance, when to make extra payments, and how much equity you're actually building over time.

The stacked bar chart in this calculator visualizes this shift year by year, so you can see exactly when the crossover happens for your specific loan.

Refinancing means replacing your existing loan with a new one, typically to get a lower interest rate, change the loan term, or switch from an adjustable to a fixed rate. The classic rule of thumb is that refinancing makes sense when you can lower your rate by at least 1%, but the real answer depends on the math.

The breakeven calculation: Refinancing has upfront costs (typically 2-5% of the loan amount). To decide if it's worth it, divide the closing costs by the monthly savings to find your breakeven period — how many months before the savings outweigh the costs.

Factors to consider:

• Rate difference — The bigger the rate drop, the faster you break even. A drop from 7% to 5.5% on a $400,000 loan saves about $400/month.
• How long you'll stay — If you plan to move in 2 years, a 3-year breakeven doesn't work. Refinancing favors borrowers who plan to stay put.
• Remaining term — If you're 15 years into a 30-year mortgage and refinance into a new 30-year loan, you're resetting the amortization clock. Your payment drops but total interest paid may increase.
• Cash-out considerations — Cash-out refinancing lets you tap home equity but increases your loan balance. Make sure the use of funds justifies the additional interest cost.

Pro tip: Use this amortization calculator to model both your current loan (from where it stands today) and a hypothetical refinanced loan. Compare total remaining interest to see the true savings after accounting for closing costs.

The difference between a 15-year and 30-year mortgage goes far beyond the monthly payment. The loan term affects your interest rate, total interest paid, monthly cash flow, and wealth-building trajectory.

Key differences:

• Monthly payment — A 15-year mortgage has significantly higher monthly payments (roughly 40-50% higher) because you're paying off the same principal in half the time.
• Interest rate — 15-year loans typically carry rates 0.5-0.75% lower than 30-year loans because the lender's risk is reduced over a shorter period.
• Total interest paid — This is where the difference is dramatic. A $400,000 loan at 7% (30-year) costs about $558,000 in total interest. The same loan at 6.5% (15-year) costs about $222,000. That's $336,000 in savings.
• Equity building — A 15-year mortgage builds equity much faster because a larger share of each payment goes to principal from day one.

Which is better? It depends on your priorities. The 15-year mortgage is better for total cost and building equity. The 30-year mortgage provides lower required payments and more monthly flexibility. A popular middle ground is taking a 30-year mortgage but making extra payments as if it were a 15-year — you get the flexibility of lower required payments with the option to accelerate when cash flow allows.

An amortization schedule is a complete month-by-month breakdown of every payment over the life of your loan. It shows exactly how much of each payment goes to interest, how much goes to principal, and what your remaining balance is after each payment.

Columns in a typical amortization schedule:

• Payment number (or date) — Which month the payment falls in
• Payment amount — Your fixed monthly payment (P&I only)
• Principal — The portion that reduces your loan balance
• Interest — The cost of borrowing for that month
• Remaining balance — How much you still owe after the payment

Practical uses:

• Tax planning — Mortgage interest is tax-deductible (if you itemize). The schedule shows exactly how much interest you'll pay each year.
• Equity tracking — Subtract the remaining balance from your home's value to see your equity at any point.
• Extra payment planning — See the impact of making extra payments at different points in the loan.
• Refinance analysis — Compare the remaining interest on your current loan vs. a refinanced loan.

This calculator shows the first 12 months in detail and yearly summaries for the rest, so you get granular near-term detail without drowning in 360 rows of data.

Amortization applies to any loan where you make regular payments that cover both interest and principal over a set period. The most common amortizing loans include:

• Fixed-rate mortgages — The most classic example. Payment stays the same for 15 or 30 years, with the interest/principal split shifting over time.
• Auto loans — Typically 3-7 year terms. Same amortization math, just shorter periods.
• Personal loans — Fixed-rate personal loans from banks or online lenders follow the same structure.
• Student loans — Federal and private student loans amortize over 10-25 years, depending on the repayment plan.
• Small business loans — SBA and conventional term loans for businesses follow amortization schedules.

Loans that do NOT fully amortize:

• Interest-only loans — You pay only interest for a period, then either refinance, pay a balloon payment, or begin amortizing.
• Credit cards — Revolving debt with variable payments and no fixed payoff schedule.
• Balloon loans — Small payments during the term with a large lump sum due at maturity.

This calculator works for any fixed-rate amortizing loan. Just enter the principal, rate, and term to see the full schedule.

The interest rate on your loan is the single biggest factor (after the principal amount) in determining your total cost of borrowing. Even small rate changes have an outsized impact because of how compounding works over long loan terms.

Rate sensitivity on a $400,000, 30-year mortgage:

• At 5% — Monthly payment: $2,147. Total interest: $373,000
• At 6% — Monthly payment: $2,398. Total interest: $463,000
• At 7% — Monthly payment: $2,661. Total interest: $558,000
• At 8% — Monthly payment: $2,935. Total interest: $657,000

Going from 5% to 8% nearly doubles the total interest paid. That's an extra $284,000 over the life of the loan. The monthly payment only increases by $788, but the cumulative effect is enormous.

What drives mortgage rates: Mortgage rates are influenced by the Federal Reserve's monetary policy, inflation expectations, the 10-year Treasury yield, and mortgage-backed securities demand. When the Fed raises rates to fight inflation, mortgage rates tend to rise. When the economy weakens and the Fed cuts rates, mortgage rates usually follow with a lag.

Strategic implications: In a high-rate environment, extra payments become even more valuable because each dollar of principal you pay off would otherwise accrue interest at a high rate. Conversely, in a low-rate environment, the opportunity cost of extra payments is higher since that money could potentially earn more in the market.

Loan amortization and DCF valuation are two sides of the same coin. Both rely on the core principle of the time value of money — the idea that a dollar today is worth more than a dollar tomorrow.

The connection:

• Amortization answers: "Given a present value (loan amount), interest rate, and term, what fixed payment do I need to make?" This is solving for the payment in a present value of annuity formula.
• DCF valuation answers: "Given a stream of future cash flows and a discount rate, what is the present value?" This is solving for the present value using the same formula family.
• Bond pricing is the middle ground — a bond pays fixed coupons (like an annuity) plus a face value (like a balloon payment). Its price is the present value of those cash flows at the market yield.

The formula used to calculate your monthly mortgage payment is mathematically identical to the formula used to value any stream of fixed future cash flows. The discount rate in a DCF model plays the same role as the interest rate in a loan — it determines how much future cash flows are worth today.

Understanding how your mortgage amortizes helps build intuition for how discounting works in valuation. Both show the same fundamental truth: money has a time cost, and compounding (whether for or against you) is the most powerful force in finance.