How mortgage amortisation actually works

An amortising loan has a payment that never changes but a composition that changes every single month. Understanding the split between interest and principal explains most of the surprising things mortgages do.

Where the payment comes from

The monthly payment is set so that the loan reaches exactly zero on the final scheduled payment:

M = P · m / (1 − (1 + m)−n)

where P is the amount borrowed, m is the monthly interest rate (the annual rate divided by twelve) and n is the total number of payments. Everything else follows from this one formula.

The split, month by month

Each month, interest is charged on whatever you still owe. Whatever is left of your payment reduces the balance. Because the balance starts large, the interest portion starts large.

On a $336,000 loan at 6.5% over 30 years, the payment is about $2,124. In month one, roughly $1,820 of that is interest and only about $304 reduces the balance — 14 cents in the dollar. The crossover, where principal first exceeds interest, does not arrive until around year nineteen. By the final year almost the entire payment is principal.

Three consequences that catch people out

Total interest can exceed the amount borrowed

On that same loan, total interest over thirty years comes to roughly $428,000 — more than the $336,000 borrowed. The sticker price of a house is not what a house costs.

Selling early means you have built less equity than you think

After five years of payments on a 30-year loan, you have paid about $127,000 and reduced the balance by roughly $21,500. The rest went to interest. Anyone likely to move within a few years should weigh that against the transaction costs of buying and selling.

Overpaying early is worth far more than overpaying late

An extra dollar of principal removes every future interest charge that dollar would have generated. Paid in year one it eliminates thirty years of compounding interest; paid in year twenty-five it eliminates five. This is why a modest, consistent overpayment early has an effect out of proportion to its size.

Refinancing: the only calculation that matters

Refinancing replaces the loan with a new one, resetting the amortisation schedule. Two figures decide whether it is worth it.

The break-even point: closing costs divided by the monthly saving. If refinancing costs $6,000 and saves $250 a month, you break even in 24 months, and it is worth doing only if you will stay considerably longer than that.

The reset: refinancing a loan you are eight years into back onto a fresh 30-year term lowers the payment partly because you have extended the debt by eight years. The monthly figure improves; the lifetime interest may not. Compare total remaining interest under both options, not just the payments.

Fifteen years or thirty?

A 15-year loan carries a lower rate and dramatically less total interest, at a much higher monthly payment. The argument for the 30-year term is not that it is cheaper — it is not — but that the lower required payment gives you flexibility, and you can always overpay voluntarily. The argument against is that most people do not.

The comparison is not purely financial either. A fixed 30-year mortgage in an inflationary period is an unusual asset: your payment is fixed in nominal terms while wages and prices rise around it, so the real burden of the debt falls every year.