Mortgage Payment Calculator
A mortgage payment is a fixed monthly amount that covers the interest first and reduces the balance with whatever is left. The split between those two changes every month while the payment itself does not, and over a long term the total interest can exceed the amount borrowed.
Payment and total interest
The monthly figure is what people compare. The interest total is the one that decides what the house cost.
The payment is P × i ÷ (1 − (1+i)^−n), where i is the monthly rate and n the number of payments. Everything else on this page falls out of that one formula.
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How the number is built
An amortising mortgage charges interest on whatever is still owed, then puts the rest of the payment against the balance. Because the balance falls, the interest portion falls with it — but the payment itself is set once, at the start, so that the loan reaches zero exactly at the end of the term.
The payment formula solves for that:
Payment = P × i ÷ (1 − (1 + i)^−n)
where P is the amount borrowed, i the monthly rate, and n the number of payments.
A worked example
Take the defaults: 300,000 borrowed at 6% over 30 years.
The monthly rate is 6% ÷ 12 = 0.5%, and there are 360 payments.
The payment is 1,798.65.
Total paid over the term is 647,515, of which 347,515 is interest — 115.8% of the amount borrowed. The interest exceeds the loan, which is the figure worth sitting with for a moment.
The first payment is 1,500 of interest and 298.65 of principal. Six per cent of 300,000 divided by twelve is 1,500, and everything left over reduces the balance.
The last payment is almost entirely principal, because there is barely any balance left to charge interest on. The payment never changed; the composition did, every single month.
What the term does
The same 300,000 at 6% over 15 years pays 2,531.57 a month and 155,683 in total interest.
Set those against the 30-year figures: 1,798.65 a month and 347,515 of interest.
The shorter term costs 41% more each month and less than half the interest overall. That is the whole trade, stated in both currencies at once — and the monthly figure is the one that decides most people’s choice while the total is the one that decides what the house cost.
The rate has the same lopsided effect. At 5% instead of 6%, the payment falls to 1,610.46 and the interest total falls to 279,767 — a single percentage point removing 67,747 of interest.
The two numbers to compare, and the one to ignore
A mortgage is usually chosen on the monthly payment, which is the number you have to find every month and the worst one to compare loans with.
Compare the interest total instead. On the defaults the 30-year loan costs 347,515 in interest and the 15-year costs 155,683 — the shorter term costs 41% more per month and saves 191,832 over the life of the loan.
Then compare the payment against what you can actually sustain, which is a different question from what a lender will approve. Lenders size loans against income; the payment has to survive a period without that income.
The number to ignore is the headline rate on its own. A lower rate with fees attached, or with a short fixed period that reverts, is not cheaper — and the only way to see that is to run both through the same formula and compare the totals rather than the rates.
Why an extra payment is worth so much
A scheduled payment is mostly interest early on. An extra payment is 100% principal. It removes that amount from the balance immediately, and with it every future month of interest that amount would have generated.
Which is why overpayments early in a term do far more than the same money later. The interest they prevent is compounded over the remaining decades, and there are more of those decades at the start.
The original data
Of the 24,971 unique videos in research/search-study-corpus.jsonl, zero have an
instruction-shaped title about mortgage payments. Real estate appears in 171 titles at a median of
27,987 views, house hacking in 1 at 60,233, and BRRRR in 5 at 242,150. The counts come from
site/rank_tools2.py.
This corpus is trading and investing content, so the absence is unsurprising and it is still worth recording. The mortgage is the largest single financial arrangement most people ever enter, its arithmetic is completely deterministic, and it appears nowhere among nearly twenty-five thousand videos about money.
The answer to the question on that chart is that the saving is real and the reset is the catch. A point off 300,000 over the full term is 67,747 of interest — but refinancing usually restarts the clock, so a loan ten years in that resets to thirty years pays a decade of front-loaded interest again. Compare the remaining schedule against the new one, not the new payment against the old payment.
When it fails
The formula prices the loan and not the transaction. Arrangement fees, valuation, legal costs and insurance sit outside it entirely, and on a refinance they are what decides whether a lower rate is actually cheaper. The same thinking applies here as to a round trip on this site’s shared series costing 2% of a median bar’s range: the headline improvement has to clear the cost of obtaining it.
The second failure is assuming the payment is the whole cost of owning. Property tax, insurance and maintenance are additional and continuing.
A third is a variable rate treated as fixed. This calculation assumes the rate holds for the term, which is not true of a tracker or a short fixed period.
A fourth is comparing monthly payments across terms. The lower payment is usually the more expensive loan.
A fifth is refinancing without comparing schedules. A lower rate on a restarted term can cost more.
And a sixth is forgetting that the payment does not adjust to your circumstances. It is fixed whether or not your income is.
Related
Mortgage covers what the loan is and how the different rate structures work. Real estate is the asset the loan is secured against. And rental property is where this payment becomes a line in a cash-flow calculation rather than a household bill.
The figure that changed how I think about term length is the interest total. Everyone compares monthly payments, because that is what you have to find each month — and the same loan over 30 years instead of 15 costs more than double the interest for a payment that is only about a third lower. Both numbers are true and only one of them is usually looked at.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.