How Mortgage Payments Are Calculated: Worked Examples From Purchase to Refinance

A fixed-rate mortgage payment depends on exactly three inputs: how much you borrow, the annual interest rate, and the number of monthly payments. Everything else a lender tells you (total interest, the amortization schedule, the payoff date) follows from those three. The examples below follow one hypothetical household through the arithmetic, and every figure was produced by the same functions that run the calculators on this site. The rates used are illustrations, not quotes of what lenders are charging today.

Setting the monthly payment

Nadia and Tom Reyes are buying a $350,000 house. They put 20% down and borrow $280,000 on a 30-year fixed loan at 6.75%. The payment that clears the loan in exactly 360 equal installments comes from the annuity formula:

M = P × r(1 + r)ⁿ / ((1 + r)ⁿ − 1)

Here P is the amount borrowed, r is the monthly rate (the annual rate divided by 12) and n is the number of payments. Step by step for the Reyes loan:

1. Monthly rate: 6.75% ÷ 12 = 0.5625%, or 0.005625 as a decimal.
2. Number of payments: 30 × 12 = 360.
3. Growth factor: 1.005625 raised to the 360th power, which is about 7.53.
4. Payment: $280,000 × 0.005625 × 7.53 ÷ 6.53, which the Mortgage Calculator evaluates without rounding as $1,816.07 a month.

Multiply by 360 and the couple will hand over $653,787 by the final payment. Subtract the $280,000 they borrowed and $373,787 of that is interest, about 1.3 times the original loan. That ratio is what a long term at a mid-single-digit rate produces; it is not a fee or a penalty, just the price of borrowing a large sum for three decades.

The same formula governs car loans, student loans and personal loans. The Loan Payment Calculator returns an identical $1,816.07 for these inputs, so either tool works for a quick check on any fixed-rate installment debt.

Where each payment goes

The payment never changes, but its split does. Each month the lender first charges interest on the balance still owed, and whatever is left of the $1,816.07 reduces the balance. In month one the interest is $280,000 × 0.005625 = $1,575.00, leaving only $241.07 for principal.

Because the balance falls slowly at first, the interest charge stays high for years. The amortization schedule for the Reyes loan shows:

• After 60 payments (five years) the balance is still $262,851.99. Of the money paid in those five years, $17,148.01 went to principal and $91,816.47 went to interest.
• The principal portion first exceeds the interest portion in payment 238, which falls in the 20th year.
• The balance does not drop to half the original loan until payment 259, in the 22nd year.

This shape matters for two decisions. Selling after a few years returns much less equity from payments than the number of payments made would suggest, because most of the money went to interest. And replacing an old loan with a new 30-year loan puts the borrower back at the interest-heavy top of a fresh schedule, a point the refinance example below makes concrete. The full month-by-month table is in the Mortgage Calculator under the results.

How the term and the rate change the cost

Keeping the $280,000 loan amount fixed, here is what happens when the Reyes household varies one input at a time. The 15-year rows show the same rate and a hypothetical lower rate, since shorter terms are often priced lower.

Loan	Monthly payment	Total interest
30 years at 6.75%	$1,816.07	$373,787
30 years at 7.25%	$1,910.09	$407,634
15 years at 6.75%	$2,477.75	$165,994
15 years at 6.25%	$2,400.78	$152,141

Half a percentage point on the 30-year loan adds $94.02 a month and roughly $34,000 over the life of the loan. Halving the term raises the payment by $661.68 but cuts total interest by more than half. Whether the shorter term is affordable is a budgeting question the formula cannot answer; what it does show is the size of the trade.

Lenders sometimes offer a lower rate in exchange for discount points paid at closing. The Federal Reserve’s refinancing guide defines a point as 1 percent of the loan amount, so one point on this loan would cost $2,800. Run the loan once at the quoted rate and once at the lower rate; the monthly difference tells you how many months it takes to earn the $2,800 back.

Down payments and the PMI dates

Suppose the Reyeses had put down only 10%. They would borrow $315,000, and at the same 6.75% over 30 years their payment would be $2,043.08 before any mortgage insurance. Conventional loans with less than 20% down usually carry private mortgage insurance (PMI), and the federal Homeowners Protection Act sets two dates for ending it, both measured against the home’s original value, here $350,000:

• Borrower-requested cancellation becomes available when the balance is first scheduled to reach 80% of original value, $280,000. On the original schedule that happens at payment 98, a little over eight years in. The borrower must ask in writing, have a good payment history and be current.
• Automatic termination applies when the balance is first scheduled to reach 78%, $273,000. That is payment 112, a little over nine years in, provided the borrower is current.

To find these dates for your own loan, divide 80% and 78% of the purchase price by the original loan amount, then look down the amortization schedule for the first month the balance falls below each figure. The Act’s automatic date follows the original schedule, so extra payments can make you eligible to request cancellation sooner, but they do not move the automatic date. FHA loans use their own mortgage insurance rules, which this calculation does not cover.

Testing a refinance

Owen owes $240,000 on his mortgage at 7.25% with 300 payments (25 years) left. A lender offers 6.25%. The Federal Reserve guide notes that refinancing fees of 3 to 6 percent of the outstanding principal are not unusual, so he assumes $7,200 in closing costs, 3% of his balance, paid in cash. His current payment for the remaining term is $1,734.74. The Refinance Calculator compares three versions of the offer:

New term	New payment	Monthly change	Break-even	Lifetime saving after costs
30 years	$1,477.72	$257.02 lower	29 months	−$18,759
25 years	$1,583.21	$151.53 lower	48 months	$38,259
20 years	$1,754.23	$19.49 higher	none	$92,206

The 30-year version has the biggest monthly saving and the fastest break-even, yet over its full life it costs Owen $18,759 more than keeping his current loan, because it adds five years of payments. Matching his remaining 25 years keeps the comparison fair: the costs are covered after four years, and he comes out ahead by $38,259 if he keeps the loan to the end. The 20-year option never “breaks even” in the monthly sense, since the payment rises slightly, but it saves the most in total. Which row is right depends on how long Owen expects to stay and how much payment he can carry, which is why the break-even month and the lifetime figure should be read together.

Before signing, the Fed guide recommends asking for any rate lock-in in writing, along with an explanation of its costs.

Comparing the mortgage with renting

Jess rents for $1,700 a month and is weighing a $325,000 home with 20% down and a 30-year loan at 6.75%. Her mortgage payment would be $1,686.36, but once property tax, insurance and maintenance are added at the Rent vs Buy Calculator defaults (1.2%, 0.5% and 1% of the home’s value a year), her first-month owner cost is $2,417.61. Keeping the remaining defaults (3% closing costs, 6% selling costs, 3% yearly growth in prices and rent, and a 4% return on the cash she would otherwise invest), the net cost of buying minus the cost of renting comes out as follows:

• Sell after 4 years: renting is cheaper by $23,618.
• Sell after 7 years: renting is cheaper by $11,265.
• Sell after 9 years: buying is cheaper by $1,328.
• Sell after 10 years: buying is cheaper by $9,041.

The crossover sits between years 8 and 9 because buying front-loads its costs: closing costs on day one, selling costs at the end, and an amortization schedule that builds equity slowly in the early years, as the Reyes table showed. Each extra year spreads those one-time costs thinner. The answer is sensitive to the price-growth and rent-growth assumptions, so treat a single run as one scenario rather than a forecast.

What these calculations leave out

• Escrowed costs. The mortgage and loan calculators show principal and interest only. Property tax, homeowners insurance, PMI and any HOA dues are added on top, and they can change from year to year.
• Adjustable rates. Every example here assumes a fixed rate. An adjustable-rate loan follows the same formula only until its first adjustment, after which the payment is recalculated on the remaining balance at the new rate.
• Extra principal. The schedules assume the scheduled payment and nothing more. Any extra principal shortens the loan and lowers total interest relative to these figures.
• Taxes and personal circumstances. Mortgage interest deductions, investment returns and moving plans differ between households. These figures are general information, not financial advice; a lender’s Loan Estimate is the document to compare offers on.