Toolhouse

What a loan really costs: the formula behind the monthly payment

A loan quote usually leads with one number, the monthly payment. It hides how much interest you will pay in total, and how the split between interest and repayment changes over time. This is general information, not financial advice.

The formula

A fixed-rate repayment loan, where every payment is the same, uses the annuity formula:

M = P × i ÷ (1 − (1 + i)^−n)

M is the monthly payment, P is the amount borrowed, i is the monthly rate (the yearly rate divided by 12) and n is the number of monthly payments. For £250,000 at 5.2% over 25 years, i is 0.052 ÷ 12 = 0.004333 and n is 300.

The result is a payment of £1,490.75 a month. Over 300 months you repay £447,226, which means £197,226 of interest. About 44% of everything you pay is interest.

Early payments are mostly interest

Each month the lender charges interest on the balance you still owe, and the rest of your payment reduces the balance. In month one the balance is £250,000, so interest is £1,083.33 and only £407.42 goes to the loan itself. As the balance falls, interest shrinks and more of each payment repays the loan. That is why the balance line in the loan calculator drops slowly at first and steepens later.

The term is a trade-off

Term Monthly payment Total interest
20 years £1,677.64 £152,632
25 years £1,490.75 £197,226
30 years £1,372.78 £244,200

Stretching the same loan from 25 to 30 years lowers the payment by about £118 a month and adds about £47,000 in interest. A longer term is not wrong, but it is a purchase, and the price is shown in the last column.

What overpaying does

Paying an extra £200 a month on the 25-year loan above clears it in 237 months, which is 19 years and 9 months. Total interest falls to about £150,290, a saving of roughly £46,900. The Toolhouse calculator does not model overpayments, but these figures use the same formula. Before you overpay, check two things: whether your lender charges an early repayment fee, and whether extra money reduces the balance straight away.

What the quote can leave out

  • Fees. Arrangement, valuation and exit fees add to the real cost. The APR figure includes many of them, so compare APRs rather than headline rates.
  • Rate changes. Many loans have a fixed rate for a few years, then move to a variable rate. Test the payment at a rate two points higher.
  • Insurance and add-ons. Some products bundle them in. Ask for the total amount payable.

The simplest comparison is the total you will have paid by the time you expect to sell or repay the loan, not the monthly figure alone.


Try it yourself: Open the loan calculator

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