Everyday Money Maths: Loans, Currency, Bills and Tips

How UK loan repayments are worked out, why your currency exchange rate is worse than advertised, how to split a bill fairly, and percentage maths explained.

How is my monthly loan repayment actually calculated?

Most personal loans and mortgages in the UK use amortisation, which means each monthly payment is split between interest and capital, but the split changes every month. Early on, most of your payment covers interest on the outstanding balance. As the balance shrinks, more of each payment chips away at the capital. This is why paying off a 25-year mortgage a few years early saves far more in interest than the same overpayment made near the end of the term.

The maths behind this uses a fixed formula based on the loan amount, the annual interest rate, and the number of payments. A common mistake is assuming interest is charged evenly across the term, then being surprised that the first two or three years of a mortgage barely dent the balance. Lenders in the UK are required to quote an APR (Annual Percentage Rate), which bundles in fees so you can compare deals fairly, but the monthly repayment figure itself comes from the amortisation formula, not the APR directly.

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Why do I never get the exchange rate I see online?

The rate quoted on Google or in the news is the mid-market rate, the midpoint between what banks buy and sell a currency for among themselves. Retail providers, high street banks, and airport kiosks add a margin on top, sometimes 3 to 5 percent, before you ever see a "commission-free" sticker. That markup is baked into the rate itself, so a 0% commission deal can still be a poor one.

Card providers add their own layer too. Many UK debit and credit cards charge a non-sterling transaction fee on top of a marked-up exchange rate when you pay abroad, and dynamic currency conversion, where a foreign till offers to charge you in pounds instead of the local currency, almost always works out worse. Paying in the local currency and letting your card provider handle the conversion is usually the cheaper route, provided your card does not charge a loading fee.

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What is the fairest way to split a restaurant bill?

Splitting a bill evenly seems simple until one person orders a starter, a bottle of wine, and dessert while another has a single main course. An even split overcharges the light eater and undercharges the big spender, which causes more quiet resentment among friends than people admit. The fairer method is itemised splitting, where each person pays for what they actually ordered, plus an even share of anything shared, such as bread or a bottle for the table.

Service charge and tipping also need factoring in properly. In the UK, a discretionary service charge of around 12.5% is often added automatically on the bill for larger groups, and it should be split proportionally to what each person spent, not evenly, otherwise the person who ordered the cheapest dish ends up subsidising everyone else's tip.

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Why do discount and tip percentages catch people out?

The most common percentage mistake is confusing "off" with "of". A jacket reduced by 30% at £80 costs £56, not £30. The discount is 30% of £80 subtracted from the original price, not the final price itself. This trips people up further with stacked discounts: two separate 20% reductions do not add up to 40% off, they compound to a 36% total reduction because the second 20% applies to an already-reduced price.

Tipping percentages cause similar confusion. A 10% tip on a £45 bill is £4.50, calculated on the bill before any service charge already added, not after. Working these out by hand under time pressure at a restaurant table is where most errors creep in, especially with odd totals like £37.60.

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