Mortgage Calculator

You’ve found a home listed at $425,000 and the lender says you “qualify,” but you’re trying to answer the real question: what will the monthly payment actually be, and how much interest will you pay over time? A mortgage payment can look manageable on paper until you factor in the principal amount, the annual rate, the loan term, and how amortization front-loads interest. A mortgage calculator turns those inputs into a clear monthly payment and an amortization schedule so you can plan your budget with fewer surprises.

What Is a Mortgage Calculator?

- Monthly principal-and-interest payment (often called P&I) - Total interest paid over the life of the loan - How each payment splits between interest and principal over time (amortization)

Context fact: In the U.S., a “conforming” conventional mortgage is commonly discussed in relation to loan limits set by the Federal Housing Finance Agency (FHFA). For 2024, the baseline conforming loan limit is $766,550 for most areas (higher in certain high-cost counties). That limit influences pricing and eligibility for many borrowers. (Source: FHFA, a U.S. government agency — Gold: [source removed])

Note: The payment computed here is typically principal + interest only. Real housing costs often also include property taxes, homeowners insurance, HOA dues, and possibly mortgage insurance.

The Formula (and What Each Part Means)

Monthly Payment = (if monthly rate > 0) principal × [mr × (1 + mr)^n] / [(1 + mr)^n − 1] else principal / n

Written cleanly:

Monthly Payment = principal * (mr * (1 + mr)^n) / ((1 + mr)^n - 1)

Where: - principal amount = loan amount = home price − down payment - mr = monthly interest rate = (annual interest rate / 100) / 12 - n = total number of payments = loan term in years × 12

Plain-English breakdown: 1. Convert the annual interest rate into a monthly decimal rate (mr). Example: 6% per year → 0.06/12 = 0.005 per month. 2. Count how many monthly payments you’ll make (n). A 30-year loan → 360 payments. 3. Compute (1 + mr)^n, which represents how interest compounds across all periods. 4. The fraction scales the payment so that, after n payments, the balance reaches zero (fully amortized). Early payments are interest-heavy; later payments are principal-heavy.

If the interest rate is 0%, the formula would divide by zero, so the fallback is simple: Monthly Payment = principal / n

Step-by-Step Examples (with Real Numbers)

### Example 1: $400,000 home, 20% down, 30 years, 6.5% 1) Loan (principal) = 400,000 − (0.20 × 400,000) = 400,000 − 80,000 = 320,000 2) mr = 6.5% / 12 = 0.065/12 = 0.0054167 3) n = 30 × 12 = 360 4) Compute growth factor: (1 + mr)^n = (1.0054167)^360 ≈ 6.99 5) Plug into formula:

Monthly Payment = 320,000 × [0.0054167 × 6.99] / [6.99 − 1] Monthly Payment = 320,000 × (0.03785) / (5.99) Monthly Payment ≈ 320,000 × 0.00632 Monthly Payment ≈ $2,022 (principal + interest)

Total paid over 360 months ≈ 2,022 × 360 = $727,920 Total interest ≈ 727,920 − 320,000 = $407,920

### Example 2: Same loan amount, shorter term (15 years), same rate (6.5%) Keep principal = 320,000 and mr = 0.0054167, but change term: 1) n = 15 × 12 = 180 2) (1 + mr)^n = (1.0054167)^180 ≈ 2.64 3) Monthly Payment:

Monthly Payment = 320,000 × [0.0054167 × 2.64] / [2.64 − 1] Monthly Payment = 320,000 × (0.01430) / (1.64) Monthly Payment ≈ 320,000 × 0.00872 Monthly Payment ≈ $2,790

Total paid ≈ 2,790 × 180 = $502,200 Total interest ≈ 502,200 − 320,000 = $182,200

Takeaway: A shorter term raises the monthly payment but can dramatically reduce lifetime interest.

### Example 3: Zero-interest special case (0% rate), $240,000 loan, 30 years This illustrates the “mr = 0” fallback. 1) principal = 240,000 2) n = 30 × 12 = 360 3) Monthly Payment = principal / n = 240,000 / 360 = $666.67

No interest is paid; every payment is pure principal.

Pro Tip: When comparing homes, keep the loan amount constant and vary only one input (rate, term, or down payment). That isolates what’s driving the payment change—especially useful when deciding whether to buy discount points or extend the term.

Common Mistakes to Avoid

When to Use This Calculator (vs. Doing It Manually)

Doing it manually is best when you want to audit a lender’s numbers or build intuition—especially around how monthly interest rate and term length change total interest. For everything else—quick scenario planning, clean payment estimates, and seeing amortization patterns—calculator-based computation is faster and less error-prone than re-deriving the annuity math by hand.

Monthly payment (PMT) = P × (mr × (1 + mr)^n) / ((1 + mr)^n − 1) when mr > 0; otherwise PMT = P / n

This mortgage calculator uses the standard fixed-rate amortization model: you borrow a principal amount P, you pay a constant monthly payment PMT for n months, and each payment covers that month’s interest plus some principal reduction. The key idea is that the loan balance evolves like a present-value problem. If the monthly interest rate is mr, then a payment made one month from now has a present value of PMT/(1+mr), a payment two months from now has present value PMT/(1+mr)^2, and so on. The original principal equals the sum of the present values of all payments:

P = PMT/(1+mr) + PMT/(1+mr)^2 + … + PMT/(1+mr)^n.

That’s a finite geometric series with ratio 1/(1+mr). Using the series sum, you get:

P = PMT × (1 − (1+mr)^−n) / mr.

Solving for PMT yields the formula shown above. When mr = 0 (a true 0% loan), the geometric-series form would divide by zero, so the payment is simply the principal evenly spread across months: PMT = P/n.

Variables and units: Home price is the purchase price of the property (typically in USD, EUR, etc.). Down payment is the upfront amount you pay (same currency). Principal P = Home price − Down payment, in currency units. Interest rate is the nominal annual rate as a percentage (for example, 6.5% per year). The monthly rate is mr = (annual_rate/100)/12, expressed as a decimal per month. Loan term is the length of the loan; if it’s given in years, then n = years × 12 months.

Unit conversions: the payment formula itself is currency-based, so it doesn’t change between imperial and metric systems. However, users often compare affordability across different home sizes. If you want to translate a price per square foot to price per square meter (or the reverse) before plugging a home price into the calculator, use 1 ft² = 0.092903 m², so $/m² = ($/ft²) ÷ 0.092903, and $/ft² = ($/m²) × 0.092903. Example: $250/ft² corresponds to 250 ÷ 0.092903 = $2,691.0/m². If a 120 m² home costs $2,691/m², the home price is 120 × 2,691 = $322,920, which then feeds into the mortgage inputs.

Worked example 1: Home price = $400,000, down payment = $80,000, so P = 400,000 − 80,000 = $320,000. Loan term = 30 years, so n = 30 × 12 = 360. Interest rate = 6.0% annually, so mr = 0.06/12 = 0.005. Compute (1+mr)^n = 1.005^360 ≈ 6.0226. Then numerator factor = mr × (1+mr)^n = 0.005 × 6.0226 = 0.030113. Denominator factor = (1+mr)^n − 1 = 6.0226 − 1 = 5.0226. Fraction = 0.030113 / 5.0226 ≈ 0.005995. Monthly payment PMT = 320,000 × 0.005995 ≈ $1,918.4 per month (principal + interest only).

Worked example 2: Home price = $650,000, down payment = $130,000, so P = 650,000 − 130,000 = $520,000. Loan term = 15 years, so n = 15 × 12 = 180. Interest rate = 4.5% annually, so mr = 0.045/12 = 0.00375. Compute (1+mr)^n = 1.00375^180 ≈ 1.9630. Numerator factor = 0.00375 × 1.9630 = 0.007361. Denominator factor = 1.9630 − 1 = 0.9630. Fraction = 0.007361 / 0.9630 ≈ 0.007644. Monthly payment PMT = 520,000 × 0.007644 ≈ $3,974.9 per month.

Edge cases and limitations: this formula assumes a fixed interest rate and fully amortizing payments made monthly. It does not include property taxes, homeowners insurance, HOA dues, mortgage insurance (PMI), or closing costs; those can materially change the true monthly outlay. It also assumes the interest rate is nominal annual with monthly compounding via mr = APR/12; some loans quote rates differently or accrue daily, which can slightly change results. Variations include biweekly payments (convert to 26 payments/year and adjust the periodic rate accordingly) and adjustable-rate mortgages (ARM), where the payment must be recalculated at each rate reset using the remaining balance as the new principal and the remaining months as the new n.

• CFPB — Owning a Home
• Consumer Financial Protection Bureau
• Investopedia
• NerdWallet
• HUD — Housing and Urban Development