How to Calculate a Mortgage Payment by Hand (and Check Your Lender)

The mortgage payment formula

Every fixed-rate mortgage payment is derived from the same mathematical formula. Once you understand it, you can reproduce a lender's number instead of accepting it on faith.

M = P × [ r(1+r)ⁿ ] / [ (1+r)ⁿ − 1 ]

Here's what each letter represents:

• M = monthly principal and interest payment
• P = loan amount — the home price minus your down payment
• r = monthly interest rate, which is the annual rate divided by 12
• n = number of monthly payments over the full term

Always use the decimal form of the rate. For example, a 6.5% annual rate becomes r = 0.065 ÷ 12 = 0.005417. A 30-year loan has n = 360.

A full worked example

Say you're buying a $450,000 home and putting 20% down. Here are the inputs:

• Down payment: $90,000
• Loan amount, P: $360,000
• Rate: 6.5% annually, so monthly r = 0.065 ÷ 12 = 0.005417
• Term: 30 years, so n = 360

Plug those into the formula:

M = 360,000 × [0.005417 × (1.005417)³⁶⁰] / [(1.005417)³⁶⁰ − 1] = $2,275.44

That's the monthly principal and interest payment before taxes, insurance, or anything else.

Now look at the first month:

• Interest = $360,000 × 0.005417 = $1,950.00
• Principal = $2,275.44 − $1,950.00 = $325.44

Yes — 86% of that first payment is interest.

Over the whole first year, the numbers are even clearer:

• Interest paid: $23,281.53
• Principal paid: $4,023.81
• Remaining balance after 12 payments: $355,976.19

Over the entire 30-year term, total interest comes to $459,160.16 — more than the $360,000 loan itself. The principal portion of your payment only exceeds the interest portion in month 233, roughly year 19.4.

The zero-rate shortcut

Before trusting any payment, it helps to know the absolute minimum. If the interest rate were 0%, the payment would simply be the loan divided by the number of months:

P ÷ n = $360,000 ÷ 360 = $1,000

At 6.5%, the actual payment is $2,275.44, so the extra $1,275.44 is the cost of borrowing. Any fixed-rate quote you see should always be above this flat paydown number.

What the formula leaves out

Lenders rarely quote just principal and interest. They typically quote PITI:

• Principal
• Interest
• Taxes — annual property tax divided by 12
• Insurance — annual homeowners insurance divided by 12

If your down payment is less than 20%, the lender may also add PMI, or private mortgage insurance. If the home is in an association, HOA dues can be another separate monthly cost.

Using the same example, say annual property tax is $4,500 and homeowners insurance is $1,500.

• Property tax: $4,500 ÷ 12 = $375/month
• Insurance: $1,500 ÷ 12 = $125/month

Add those to the principal and interest payment:

$2,275.44 + $375 + $125 = $2,775.44 full PITI payment

That's still before any PMI or HOA dues, which would raise the total further.

Why the first year has so little principal

At the start of the loan, interest is charged on the entire $360,000 balance every month. Your $2,275.44 payment first covers that interest charge, and only the remainder reduces the balance.

Because the early principal payments are so small, the balance falls slowly, keeping the next month's interest charge nearly as high. That's why amortization is front-loaded: the first year pays $23,281.53 in interest and only $4,023.81 toward principal. You don't reach the point where more of your payment goes to principal until month 233.

This isn't a mistake by the lender — it's how compound interest works over a long amortization schedule. If you want to see the exact payoff schedule, the Amortization Calculator lists every payment so you can check month 1, month 12, or month 233 yourself.

How to check a lender's quote

A lender's quote should be easy to verify if you use the exact same inputs. Here's the process:

1. Use the same loan amount, same annual rate, and same term the lender used.
2. Run the formula above, or enter the numbers into the Mortgage Payment Calculator.
3. Compare the principal-and-interest number first.
4. Then add taxes, insurance, PMI, and HOA separately from the loan estimate.
5. If there's still a discrepancy, ask the lender what extra line items are included and whether the rate or loan amount matches your inputs.

Small differences can also come from rounding or from the lender calculating interest daily during the first partial month. But a large unexplained gap usually indicates an added fee or a different rate.

When to just use the calculator

Doing the math by hand is worthwhile once, so the payment stops feeling like a black box. After that, testing different down payments, rates, and terms is much faster with a tool. The Mortgage Payment Calculator runs this exact math with taxes and insurance included. Before you commit to a sale price, the Home Affordability Calculator can help you choose a number that fits your budget.