The arithmetic
Why the early payments barely touch the balance.
A repayment mortgage is level-payment amortisation: the monthly figure stays the same across the term, but its composition changes. Interest is charged on whatever is currently outstanding, so at the start almost all of the payment is interest and very little of it reduces the debt.
As the balance falls, the interest portion falls with it and more of each unchanged payment goes to capital. The effect compounds, which is why the balance drops slowly for the first several years and then quite quickly at the end — and why an overpayment made early is worth far more than the same overpayment made late.
It also explains why the term has such a large effect on total interest and such a modest one on the monthly figure. Extending a term spreads the capital over more months, but every one of those extra months carries interest on a balance that is now falling more slowly.
→Total interest is the figure that reveals the cost of a long term; the monthly payment conceals it.
→An overpayment reduces interest for the entire remaining term, not just for the month it is made.