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The cost of exchange

A bureau sells high and buys low, then adds a fee. Work out what changing money really costs: the side of the board, the round trip, the cross rate.

  • Money
  • Untimed
  • Endless levels

How it plays

A money changer shows two prices for each currency: the price it sells at, and the lower price it buys back at. You always get the worse one — the gap is its fee, even when the sign says "no commission".

Levels go from which side of the board you deal on, to the round trip (change and change back), to a commission on top of a marked-up rate measured against the mid-market rate, to cross rates through a third currency, with and without spreads.

The foreign currencies are invented and every rate is made up, so nothing here is a quote. Answers are to 2 dp and a typed answer within 0.01 counts. The wrong options are the real slips: the wrong side of the board, the mid rate used, the spread divided by the wrong price.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This makes working out the real cost of a currency exchange from its rates and fees quicker and surer. It claims nothing wider and is not financial advice.

Learn

How to get better at the cost of exchange: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Decide which way the money goes. If you are getting the foreign currency, the bureau is selling it to you; if you are handing it back, the bureau is buying it.
  2. Take the rate that is worse for you: the higher selling price when you buy, the lower buying price when you sell. The bureau never gives you the better one.
  3. Rates are in your money per unit of the foreign one. To get foreign units, divide your money by the rate; to get your money back, multiply the units by the rate.
  4. For a cost, value what you end up with at the mid-market rate and take it from what you started with. Fees come off before converting, exactly as the question says.

Techniques and tricks

  • Divide to go out, multiply to come back

    Going out you are buying units, so divide your money by the price of one. Coming back you are selling units, so multiply them by what one fetches.

    e.g. ₹10,000 at a selling price of ₹12.60 is K 793.65; K 500 at a buying price of ₹12.00 is ₹6,000.

  • The round-trip share

    Change and change straight back, and you lose the share (sell − buy) ÷ sell of what you started with.

    e.g. Sell 12.60, buy 12.00: 0.60 ÷ 12.60 = 4.76%, so ₹10,000 comes back as ₹9,523.81, a loss of ₹476.19.

  • Markup and commission nearly add

    A commission and a rate markup together cost a little less than their sum, because the markup only applies to what is left after commission. Use the sum to check the size, then work it exactly.

    e.g. Mid 20.00, sell 20.30 (1.5%), 1% commission on ₹20,000: cost ₹492.61, or 2.46%, not quite 2.5%.

  • Cross rate is a ratio

    To turn one foreign currency into another, go through your own: multiply by the first one’s price, then divide by the second’s. The cross rate is the first price over the second.

    e.g. 1 K = ₹12.00 and 1 Z = ₹8.00, so 1 K = 1.5 Z and K 200 = Z 300.

  • Both spreads on a cross

    Through a bureau you pay twice: it buys your first currency at its low price and sells you the second at its high price.

As the levels climb

  • The kinds unlock one at a time: which side of the board and changing back at level 0; the round trip at level 1; a fee on top at level 3; a cross rate at level 5; a cross with spreads at level 7.
  • Between unlocks, and for ever after, the sums grow and the spreads widen, from at most 4% between the two prices up to 7%. Wider spreads make the wrong-side lure further from the truth, and easier to spot.
  • The fee questions often add a fixed charge to the percentage commission. Take both off before converting; the fixed charge does not scale with the sum.
  • The cross questions have no board at first, only mid rates. When the spreads arrive, it is the same ratio with the worse price on each leg.

Traps to avoid

  • The wrong side of the board: dividing by the buying price when you buy, or multiplying by the selling price when you sell. It always gives you more than you would really get.
  • The mid rate used: what you would get with no spread at all. It is the yardstick for the cost, never the deal itself.
  • The round-trip loss with the gap divided by the buying price instead of the selling price. It overstates the loss a little.
  • The commission alone given as the cost, forgetting that the marked-up rate is a fee too.
  • A cross rate turned upside down, the second price over the first, or the two prices multiplied. Check the units: K × (₹ per K) ÷ (₹ per Z) leaves Z.

How to practise

  • Use “Kinds of question” to drill the round trip and the fee until the share formula is automatic; they are where the real cost hides.
  • Switch Answer by to “Typing the answer”; a typed answer must be within 0.01, so you must use the right price on every leg.
  • Pick your own Currency. The foreign currencies are made up, but the arithmetic of a board is the same as at any real bureau.

Levels

It is untimed unless you turn the clock on. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

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