How to Calculate Mortgage Payments (The Monthly Payment Formula)

The short answer

Use the amortization formula: M = P × r(1+r)^n / ((1+r)^n − 1), where P is the loan principal, r is the monthly interest rate, and n is the number of monthly payments. For a $300,000 loan at 4.5% over 30 years, that returns about $1,520 a month.

The formula assumes a fixed rate and equal monthly payments. It gives you the principal-and-interest payment; taxes, insurance, and fees are separate unless your calculator folds them in.

• P = loan principal (the amount you borrow)
• r = monthly interest rate (annual rate ÷ 12, for a US-style APR)
• n = total payments (years × 12)
• M = the fixed monthly principal-and-interest payment
• For $300k at 4.5% over 30 years: M ≈ $1,520.06

The mortgage payment formula, explained

The formula is the present value of an annuity solved for the payment. In plain terms, it finds the fixed amount that, invested at the loan's rate month after month, exactly repays the principal plus all the interest by the final payment.

Every part has a job. P sets the size of the debt, r sets how fast it grows each month, and n sets how many chances the payment has to tame that growth. Lengthen the term and the monthly payment drops, but total interest rises.

What the symbols mean

P (principal): the starting loan balance, before any fees are added. A bigger P means a bigger payment, all else equal.

r (rate): the interest applied each period. This is the monthly rate, so an annual figure must be converted before it enters the formula.

What 'with interest' actually means

The interest in the formula is not the annual percentage quoted by a lender — it is the rate for a single month. For a US APR, you divide the annual rate by 12 (4.5% becomes 0.00375 per month). Get this conversion wrong and the payment is off by hundreds of dollars.

Other rate systems convert differently. European nominal and Brazilian TAXA rates are compounded, so the monthly rate is (1 + annual)^(1/12) − 1 rather than a straight division. The calculator handles all three, which matters more than the headline number.

How to calculate mortgage payments by hand

Pick the principal, turn the annual rate into a monthly rate, set n = years × 12, then work the formula step by step. It is tedious but transparent: you see exactly where the payment comes from and can sanity-check a lender's number.

A calculator spares you the exponent arithmetic, but doing one loan by hand once is the fastest way to stop fearing the formula. The steps below use the same numbers the tool defaults to.

Step by step

Convert the rate: 4.5% ÷ 100 = 0.045, then ÷ 12 = 0.00375 monthly. Set n = 30 × 12 = 360 payments.

Compute (1+r)^n, multiply by r, divide by ((1+r)^n − 1), then multiply by P. The result is the monthly payment, about $1,520 for these inputs.

A worked example

With P = 300000, r = 0.00375, n = 360: (1.00375)^360 ≈ 3.847. So M = 300000 × (0.00375 × 3.847) / (3.847 − 1) ≈ 300000 × 0.01442 / 2.847 ≈ 1520.

Multiply that by 360 payments and you get about $547,223 total — roughly $247,000 of that is interest. The gap between the loan and the total is the cost of spreading it over 30 years.

How to calculate mortgage payments in Excel

Excel has a built-in function: =PMT(rate, nper, pv). Use rate as the monthly rate (e.g. 0.045/12), nper as the number of payments (360), and pv as the negative loan amount. The result is the monthly payment, returned as a negative number by convention.

You can also lay out the full schedule with rows for each month, which makes the interest-versus-principal split visible — exactly what the calculator's amortization table does for you automatically.

• =PMT(0.045/12, 360, -300000) returns about 1520.06
• Use -pv (negative principal) so the payment comes back positive if you prefer.
• Wrap it in ABS() to drop the sign: =ABS(PMT(0.045/12,360,-300000))
• Build a month-by-month table with IPMT and PPMT for the interest and principal pieces.

Why your first payment is mostly interest

Interest is charged on the balance you still owe, and at the start that balance is the entire principal. So your first payment covers a large slice of interest and only a sliver of principal — even though the dollar amount never changes.

Each month the principal shrinks, so the interest charge shrinks with it and more of the same payment goes to principal. By the end, almost the whole payment is principal. This slow flip is amortization, and it is why early overpayments save so much.

Fixed vs variable, and the rate-system trap

A fixed-rate loan uses one rate for the whole term, so the formula above applies directly. A variable loan changes its rate periodically; you can model a single expected change, but no static formula captures a rate that moves on its own.

Even within 'fixed', the quoted rate can mean different things by country. The calculator exposes three systems — US APR, EU nominal, and Brazil TAXA — because mixing them up changes the monthly payment by a noticeable amount.

APR vs nominal vs TAXA

US APR includes fees and divides the annual rate by 12 for the monthly figure. EU nominal quotes the rate without fees and compounds it. Brazil's TAXA compounds annually before the monthly step.

At 10% annual, the three give slightly different monthly rates, so the same '10%' can mean different payments depending on which system your lender uses. Pick the one on your paperwork.

Why it matters for your payment

A borrower who enters a nominal 3.5% as if it were a US APR underpays the true monthly figure by a small but real amount — the calculator's three modes exist precisely to stop that error.

When comparing offers, compare like with like: APR against APR, nominal against nominal, TAXA against TAXA.

What the calculator includes — and what it leaves out

This calculator returns the monthly principal-and-interest payment, the total interest, the total of all payments, an effective APR that folds in any closing fees, and a full amortization schedule you can export to CSV.

It does not include property tax, insurance, or mortgage-insurance premiums, and it performs no live currency conversion — you pick the currency and the numbers are treated as already in that currency. It is an estimate, not a loan commitment.

• Included: monthly P&I, total interest, total paid, effective APR, amortization table, CSV export.
• Not included: taxes, insurance, PMI, or any live exchange-rate conversion.
• Closing fees are optionally added and surface as the effective APR, not as a higher monthly payment.
• Always confirm final numbers with your lender — this is a planning tool, not an offer.

Reading the amortization schedule

The schedule lists every payment with how much is interest, how much is principal, and what balance remains. Early rows are almost all interest; later rows are almost all principal. Watching the balance column fall is the clearest picture of how amortization works.

Export it to CSV and you can total the interest for any date range, or see exactly when you cross the point where principal overtakes interest — useful for deciding whether refinancing is worth it.

When to use the calculator before you borrow

Run the numbers before you shop, not after. Knowing the monthly payment for a few rate and term combinations tells you what price range is sane, and the schedule shows how much extra a longer term really costs in interest.

It is also the fastest way to check a lender's quote: if their payment does not match the calculator on the same inputs and rate system, you know to ask why. Everything runs in your browser, so you can comparison-shop privately.

• Test several rates and terms to find a payment you can carry.
• Compare a lender's quote against the same inputs in the calculator.
• Export the schedule to see lifetime interest before you commit.
• Nothing is uploaded — your figures stay in the browser tab.

Frequently asked questions