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The Airport Money Trap

Algebra

Exchange Β£100 into euros and straight back, and you won't get Β£100. How much vanished, where did it go, and why does '0% commission' cost more than the place charging a fee?

Where this idea comes from

Start here β€” these are the sources that inspired this exploration.

Introduction

Every currency desk shows two rates β€” one for buying, one for selling β€” and the gap between them is where the money goes. Collect today's rates from several places (the true mid-market rate online, a bank, a travel card, an airport desk) and run the same brutal test on each: convert Β£100 out and straight back. The round trip should return Β£100; the shortfall measures each provider's real cost, whatever their posters promise. Airport desks have been caught charging the equivalent of 14% or more this way. The exploration is about the PERCENTAGES β€” how spreads compose, why two 3% losses don't add to 6%, where a flat fee beats a percentage β€” not a consumer rant; the maths is what exposes the trick.

Guiding Questions
  • Collect today's buy and sell rates for one currency pair from four or five providers, plus the mid-market rate online. Lay them side by side β€” what do you notice about where each provider sits around the 'true' rate?
  • Run the round trip: Β£100 out and straight back with each provider. Rank them by what survives. How does a '0% commission' desk compare with one charging an explicit fee?
  • Write the round trip as a function: if a provider takes p% on each direction, what fraction of your money survives both? Why is the loss not simply 2p%?
  • Some providers charge a flat fee instead of (or as well as) a worse rate. Find the crossover: for what amounts is the flat-fee provider the better deal? Show it with a graph.
  • Your provider list is a sample. Choose something about the trade to vary β€” amount, currency pair, weekday vs weekend, online vs in person β€” and investigate whether the ranking of providers is stable.
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Key Mathematical Concepts
Financial Mathematics Consumer Mathematics Exchange Rates Functions Percentages
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