Mortgage Math: What a Point of Rate Does to a Payment
Amortization is the most consequential formula most people never learn. Here is what one point of mortgage rate does to a payment, a budget, and thirty years of interest, in worked examples you can redo yourself.
The Formula That Prices the Roof Over Your Head
A standard American mortgage is a fixed rate amortizing loan, one interest rate locked for thirty years and one identical payment every month, sized so the balance hits exactly zero at payment number 360. Each payment splits into two parts, interest, computed as the monthly rate times whatever balance remains, and principal, whatever is left over, which reduces the balance for next month. Three inputs drive everything, the loan amount, the rate, and the term, and because the formula is exponential rather than linear, small changes in the rate produce payment changes that surprise almost everyone the first time they run the numbers. This article is just those numbers, run honestly.
One Loan, Four Rates
Take a 400,000 dollar loan over thirty years, roughly what a 500,000 dollar house with 20 percent down requires, and move only the rate.
| Rate | Monthly payment | Total interest over 30 years |
|---|---|---|
| 4.5% | 2,027 | 330,000 |
| 5.5% | 2,271 | 418,000 |
| 6.5% | 2,528 | 510,000 |
| 7.5% | 2,797 | 607,000 |
Read the right column twice. At 6.5 percent, the borrower pays 510,000 dollars of interest to borrow 400,000, more for the money than for the house share it financed. And the two point trip from 5.5 to 7.5 percent, exactly the range mortgage rates have occupied since 2022, adds 526 dollars a month and roughly 189,000 dollars of lifetime interest on the identical loan. Nothing about the house changed. Only the price of money did.
The Ten Percent Rule
Near current levels a clean rule of thumb falls out of the table, every full point of rate moves the payment on a given loan by roughly 10 percent. It also works in reverse, and the reverse is where housing markets are made. Flip the question to a buyer with a fixed budget of 2,500 dollars a month for principal and interest, at 4.5 percent that budget supports a loan of about 493,000 dollars, at 5.5 percent about 440,000, at 6.5 percent about 395,000, and at 7.5 percent about 358,000. The same paycheck bids for 27 percent less house at 7.5 than at 4.5, which is why home prices, sales volumes, and builder incentives all dance to the Federal Reserve's tune, every rate move silently reprices what every buyer in the country can offer.
One point of rate moves a payment by about 10 percent, and it moves how much loan a fixed budget supports by about 10 percent in the opposite direction. That single fact explains most of what happened to American housing between 2021 and 2026.
Your First Payment Is 86 Percent Interest
On the 400,000 dollar loan at 6.5 percent, the first month's payment of 2,528 dollars contains 2,167 dollars of interest and just 361 dollars of principal, about 86 percent interest. This is not a lender trick, it is arithmetic, interest accrues on the outstanding balance and the balance starts at its maximum, but the consequences are worth internalizing. After five full years the borrower has paid roughly 151,700 dollars and still owes about 374,500, meaning only 25,500 dollars of principal got retired. Early in a mortgage, ownership is overwhelmingly a rental arrangement with your bank, a fact that quietly powers the rent versus buy math we work through in a companion piece, and it is why extra principal payments made early beat the same dollars paid late.
Points, Buydowns, and the Refi Trigger
Three levers let borrowers trade money for rate. A discount point costs 1 percent of the loan upfront and typically shaves about a quarter point off the rate, so 4,000 dollars to go from 6.5 to 6.25 percent saves 65 dollars a month and takes roughly 61 months to break even, worthwhile only if you will keep the loan well past year five. Temporary buydowns, like the popular two one structure, prepay a lower rate for the first year or two and are really a marketing tool sellers and builders fund to make payments look palatable. Refinancing replaces the whole loan when rates fall, at a cost of roughly 2 to 5 percent of the balance, dropping our loan from 6.5 to 5.75 percent saves 194 dollars a month, so an 8,000 dollar refi breaks even in about 41 months. The folk rule that a refi needs a three quarter to full point improvement exists because of exactly this breakeven math.
Where Rates Sit Right Now
As of mid July 2026 the Freddie Mac survey puts the average thirty year fixed rate at 6.55 percent, up from 6.49 the week before, drifting higher on sticky inflation and rising Treasury yields, and rates have held the mid 6s for most of the year. Context matters in both directions, the pandemic low of 2.65 percent in January 2021 was the cheapest mortgage money in American history and an anchor that still distorts everyone's sense of normal, while the long run average since 1971 sits near 7.7 percent. A 6.5 percent mortgage is historically ordinary. It only feels punishing because it is attached to record home prices, which is the subject of our housing shortage piece, and because an entire generation locked in 3 percent and cannot afford to let it go.
The Bottom Line
The payment formula is exponential, so rates matter more than almost anyone intuits, one point moves a payment about 10 percent, two points moved the typical buyer's budget by more than a quarter, and the interest on a 6.5 percent loan exceeds the principal borrowed. Learn the table above and you can sanity check any mortgage, price any refinance, and understand why the entire housing market holds its breath before every Fed meeting. The house is the asset, but the mortgage is the trade.