POP

E1.16 Money

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01 — Explanation

How do I convert between currencies?

Multiply or divide by the given exchange rate — the key is checking which direction the rate is written in. If " $\$ 1=€0.92 $", every dollar you have becomes$ 0.92 $euros, so you **multiply** dollar amounts by$ 0.92$ to reach euros (and divide to go the other way).

02 — Explanation

How do I apply money calculations to real-life contexts like sharing a bill?

Apply the four operations exactly as in any other context, then present the final answer to the correct accuracy for currency.

Examiner Tip: Money answers must always be given to exactly 2 decimal places — the smallest coin/cent unit — even when that means writing a trailing zero, e.g. $€80.50$ , not $€80.5$ .

Worked Example

The exchange rate is $\$ 1 = €0.92 $. Maria has$ \ $350$ and wants to convert it to euros to split equally between $4$ friends.

(a) How many euros does she receive in total?

(b) How much does each friend receive, in euros?

Convert dollars to euros: $350 \times 0.92 = €322$ .
Divide equally among $4$ friends: $322 \div 4 = €80.50$ each.

03 — Explanation

How do I handle a currency exchange that charges a commission or fixed fee?

Apply the fee to the amount before exchanging (if it's taken from the starting currency) or after exchanging (if it's taken from the currency received) — the wording of the question tells you which, and getting this order wrong changes the final answer.

Worked Example

A bank charges $2\%$ commission on the amount exchanged, taken before the conversion. Using the rate $\$ 1=€0.92 $, find how many euros a customer receives for$ \ $500$ .

Deduct the $2\%$ commission from the dollar amount first: $500 \times (1-0.02) = 500\times0.98=\$ 490$.
Convert the remaining amount to euros: $490 \times 0.92 = €450.80$ .

04 — Explanation

How do I convert an amount through two currencies in sequence (a double conversion)?

Apply each exchange rate one after the other, in the order the money actually moves, treating the result of the first conversion as the input to the second.

Worked Example

$\$ 1 = €0.92 $and$ €1 = £0.85 $. Convert$ \ $600$ directly to pounds.

Convert dollars to euros: $600 \times 0.92 = €552$ .
Convert that result to pounds: $552 \times 0.85 = £469.20$ .

Examiner Tip: Don't try to multiply the two exchange rates together to make one "shortcut" rate unless the question explicitly gives you a direct dollar-to-pound rate — work through the intermediate currency step by step to avoid compounding a rounding error.

05 — Explanation

What if I'm given the rate the "wrong way round" for what I need to calculate?

Exchange rates are sometimes quoted the opposite way to how the question needs them (e.g. " $€1 = \$ 1.09$" when you actually need to convert dollars to euros). In that case, divide by the rate instead of multiplying — dividing by "how many euros one dollar buys" undoes the direction and gets you back to dollars, and vice versa. Always sanity-check your answer's size: converting a strong currency into a weaker one should give a bigger number, and converting the other way should give a smaller one.