numberrule

Every formula, written out

What actually decides a mortgage payment

A mortgage payment comes from exactly three numbers: how much you borrowed, the rate, and how long you have to repay it. Everything else on a lender's quote — insurance, taxes, fees — sits alongside the loan rather than inside it.

The formula behind it is unforgiving in a specific way. Small changes to the rate move the payment a little and the total repaid a great deal, and where the money goes in the first few years is nothing like what most people picture.

The payment is the same every month; what it buys is not

A repayment mortgage is designed so that the monthly amount never changes while the balance falls to zero exactly at the end of the term. That fixed payment is split between interest and principal, and the split moves month by month.

Interest each month is simply the outstanding balance times one month of the rate. At the start the balance is nearly the whole loan, so nearly the whole payment is interest. As the balance falls the interest portion falls with it, and the principal portion grows to fill the gap.

On $300,000 at 6.5% over thirty years the payment is $1,896.20. In the first month, $1,625.00 of that is interest and only $271.20 comes off what you owe. That is the number that surprises people: after a full year of payments the balance has barely moved.

Borrowed $300,000 at 6.5% over 30 years

Payment $1,896.20 a month

Month 1 $1,625.00 interest, $271.20 principal

Total interest over the term $382,633.47

Total repaid $682,633.47

Work it out: Mortgage Payment Calculator →

Over a full term, interest can exceed the loan

That same loan repays $682,633.47 in total — more in interest than the house cost. It is not a sign of anything unusual; it is what thirty years of compounding does at that rate, and it is why the term matters as much as the rate.

A one point rise, from 6.5% to 7.5%, takes the payment from $1,896.20 to $2,097.64. That is about $200 a month, which sounds survivable. Over the full term it is $72,518 more interest, which does not.

This asymmetry — a modest change in the monthly figure, a large change in the total — is the single most useful thing to hold on to when comparing offers. The monthly payment is what you can afford; the total repaid is what it costs.

Work it out: Amortization Schedule Calculator →

Why a small overpayment is worth so much

An extra payment goes entirely against the principal. It does not just save you that money — it removes the interest that balance would have generated in every remaining month, and that saving compounds for the rest of the term.

Paying $200 a month extra on the loan above costs $55,400 over the years you keep it up, and saves $103,448.79 in interest. It also clears the mortgage six years and eleven months early. That is not a clever product; it is arithmetic, and it is available on almost any loan.

Two things to check before relying on it. Some lenders hold overpayments against the next instalment rather than applying them to the principal, which achieves nothing, and some fixed deals carry early repayment charges. Both are worth confirming in writing rather than assuming.

$200 a month extra on $300,000 at 6.5%

Extra paid in $55,400.00

Interest saved $103,448.79

Paid off 6 years 11 months early

Work it out: Extra Mortgage Payment Calculator →

Shorter term, or longer term and overpay?

A fifteen year term on the same $300,000 — and shorter terms usually carry a slightly better rate, say 5.9% — costs $2,515.39 a month against $1,896.20. That is $619.19 more, and it saves $229,863.03 in interest. Roughly two pounds or dollars saved for every extra one paid.

The arithmetic clearly favours the shorter term. The judgement does not always follow, because a shorter term is a contractual commitment and a voluntary overpayment is not. Take the thirty and overpay and you capture most of the saving while keeping the ability to stop in a bad month; take the fifteen and the higher payment is due whatever happens.

Which is right depends on how secure the income is and how much else is competing for the money. What the numbers do settle is that the difference is large enough to be worth deciding deliberately rather than by default.

Work it out: 15 vs 30 Year Mortgage Calculator →

Points, and the break-even nobody works out

Buying points means paying a lump sum up front to lower the rate. It is a straightforward trade — money now against a smaller payment every month — and it comes down to a single question: how long before the saving repays the cost?

A point is typically one per cent of the loan and usually buys a quarter point off the rate. On $300,000 that is $3,000 for a lower payment, and the break-even usually lands somewhere between four and six years.

So the answer depends entirely on how long you keep the loan. Stay past the break-even and points are free money; move or refinance before it and you have simply paid the lender extra. Anyone who cannot say roughly how long they intend to stay should not be buying points.

Work it out: Mortgage Points Calculator →

Questions

Why is my first mortgage payment almost all interest?

Because interest is charged on the outstanding balance, and at the start the balance is the whole loan. On $300,000 at 6.5% the first payment is $1,625 interest and $271 principal. The split shifts steadily as the balance falls.

How much does one per cent on the rate cost?

On a $300,000 thirty-year loan, going from 6.5% to 7.5% adds about $200 a month — and around $72,500 over the full term. The monthly difference always understates the total.

Is it worth overpaying a mortgage?

Usually, and by more than people expect. $200 a month extra on a $300,000 loan at 6.5% saves over $103,000 in interest and clears it nearly seven years early, because every overpayment removes interest from every remaining month.

Should I take a 15-year mortgage or a 30-year?

The 15-year saves far more interest, but it is a commitment. Taking the 30-year and overpaying captures most of the saving while leaving you able to stop in a difficult month. How secure the income is decides it.

Are mortgage points worth buying?

Only if you keep the loan past the break-even, which is typically four to six years. Move or refinance before then and the up-front cost is simply lost.

Does the quoted payment include taxes and insurance?

Sometimes, and it is worth asking. The loan itself is principal and interest; anything a lender bundles in alongside it is a separate cost that will move independently of the mortgage.

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