An amortising loan is repaid in equal instalments, each covering the interest accrued that month plus a slice of the outstanding principal. The payment size is fixed; the split between interest and principal is not.
P is the principal, i the monthly rate (annual rate divided by twelve) and N the total number of payments.
Early payments are almost all interest
On a 25-year loan at 5.5%, the first payment is roughly two thirds interest. The balance shifts gradually and only crosses over to majority-principal around the halfway point. This is why paying off a loan a few years early saves far less than the remaining years suggest — most of the interest has already been paid.
Term versus payment
Extending the term reduces the monthly payment but increases the total interest sharply, because the balance stays high for longer. On £250,000 at 5.5%, moving from 25 to 35 years cuts the payment by roughly 12% while adding well over £100,000 in interest.
Overpayments
An extra payment goes entirely against principal, so it removes all the future interest that principal would have generated. Early overpayments are dramatically more effective than late ones. Check whether your lender charges early repayment penalties first.
What the formula ignores
Real loans add arrangement fees, insurance, taxes and sometimes variable rates. The APR is the figure designed to include most of these, and it is the one to compare between lenders. This calculator gives the pure amortisation figure and is not financial advice.