How Mortgage Payments Are Calculated

Every fixed-rate mortgage payment in the country comes out of one formula. It looks intimidating written down, but it answers a simple question: what constant monthly amount, paid for exactly this many months, pays off this balance at this rate and leaves nothing behind?

Once you can read the formula, a few things that seem arbitrary — why the first years barely dent the balance, why a small rate change moves the payment so much, why 15-year loans cost so much less in total — stop being mysterious.

The amortization formula

M = P × [ i(1 + i)^n ] / [ (1 + i)^n − 1 ]

• M is the monthly payment for principal and interest
• P is the amount borrowed
• i is the monthly rate: the annual rate divided by 12
• n is the total number of payments (years × 12)

Take a $400,000 loan at 6.5% over 30 years. The monthly rate is 0.065 ÷ 12 = 0.0054167, and n is 360. Run it through and you get about $2,528 a month in principal and interest.

Two conversions cause most hand-calculation errors: the rate must be monthly, not annual, and n counts months, not years. Get either wrong and the answer will be off by a factor that looks almost plausible, which is worse than being obviously wrong.

Why your early payments are nearly all interest

The payment stays constant, but its composition changes every single month. Each month the lender charges interest on the balance that is currently outstanding, and whatever is left over reduces the principal.

Month one on that $400,000 loan:

• Interest: $400,000 × 0.0054167 = $2,167
• Principal: $2,528 − $2,167 = $361

You paid $2,528 and your debt fell by $361. About 86% of that first payment was rent on the money.

Month two, the balance is $361 lower, so the interest is fractionally smaller and the principal portion fractionally larger. That shift compounds. By roughly year 18 of a 30-year loan at this rate, the split finally crosses the halfway mark.

This is why paying extra early is disproportionately effective: a dollar of extra principal in year one removes that dollar's interest for all 359 remaining months. The same dollar in year 28 saves almost nothing. It is also why refinancing resets more than people expect — you restart at the steep end of the curve. The refinance calculator compares the new payment against the interest you give up by restarting.

What else is in the monthly bill

The formula above produces principal and interest only. Lenders quote PITI, and the other letters are not small:

• Taxes. Property tax varies enormously by jurisdiction and is usually escrowed monthly.
• Insurance. Homeowner's insurance, also typically escrowed.
• Mortgage insurance. Generally required below 20% down, and it buys you nothing — it protects the lender.
• HOA dues, where applicable, paid separately but budgeted the same way.

It is common for the true monthly cost to land 25–35% above the principal and interest figure. Our mortgage payment calculator breaks the payment into these components rather than quoting the formula alone, because the formula-only number is the one that gets people into trouble.

Closing costs are a separate shock — typically 2–5% of the price, due up front. The closing costs calculator itemises them.

Why small rate changes move the payment so much

The rate sits inside an exponent raised to the 360th power, so its effect is not proportional. On that same $400,000 loan over 30 years:

Rate	Monthly P&I	Total interest paid
5.5%	$2,271	$417,560
6.5%	$2,528	$510,080
7.5%	$2,797	$606,920

One percentage point costs roughly $257 a month — and about $92,000 over the life of the loan. That is the single strongest argument for shopping lenders rather than accepting the first quote.

Term length works the same way. A 15-year loan at the same rate has a much higher monthly payment but dramatically less total interest, because you are borrowing the money for half as long.

Checking a lender's number yourself

You do not need to reproduce the formula by hand to catch an error. Two checks cover most cases.

The first-month interest check. Multiply the loan balance by the annual rate and divide by 12. That is the interest portion of payment one. If the quoted total payment is not comfortably above that figure, something is wrong — either the payment cannot amortise the loan, or the quote excludes escrow.

The total-paid check. Multiply the monthly payment by the number of payments. On a 30-year loan at typical rates, the total is usually somewhere near double the amount borrowed. If it comes out far below that, the quote is probably missing something.

Before shopping at all, it is worth knowing what a lender will actually approve. That is driven less by the payment formula than by your debt-to-income ratio, and the home affordability calculator works backwards from income to a defensible price range.

The buy-versus-rent question the formula cannot answer

Amortization tells you what a payment is. It says nothing about whether buying is the better financial decision, which depends on how long you stay, what the alternative rent costs, transaction costs on both ends, and what your down payment would have earned elsewhere — that last part being pure compound interest.

The rent vs buy calculator models the break-even horizon, which for most US markets lands somewhere in the range of five to seven years.

For neutral primary-source guidance on comparing offers, the CFPB's Owning a Home tools show how to read a Loan Estimate line by line, and Freddie Mac's rate survey gives a reference point for whether a quoted rate is competitive.