POP

C1.16 Money

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01 — Explanation

How do I convert between currencies using an exchange rate?

An exchange rate states the value of one currency in terms of another, e.g. $\$ 1 = 0.85$ Euros.

\text{Amount in Currency B} = \text{Amount in Currency A} \times \text{Exchange Rate}

\text{Amount in Currency A} = \text{Amount in Currency B} \div \text{Exchange Rate}

Example (a): convert $\$ 320 $to Euros using$ \ $1 = 0.85$ Euros: $320 \times 0.85 = €272$ .

Example (b): convert $€510$ back to US Dollars: $510 \div 0.85 = \$ 600$.

Common Slip

multiplying in both directions regardless of which way the conversion goes. Only multiply when converting into the currency the rate is quoted in; divide when converting the other way.

02 — Explanation

How should money answers be rounded?

Money is always rounded to 2 decimal places, since most currencies split into $100$ subunits (cents, pence, etc.):

Calculator display	Correctly rounded
$38.5$	$\$ 38.50$
$12.786$	$\$ 12.79$
$200$	$\$ 200.00$

Example: the exchange rate is $\$ 1 = 74.30 $Rupees. Convert$ \ $45$ to Rupees, to the nearest Rupee.

Multiply: $45 \times 74.30 = 3343.5$ .
Round to the nearest whole Rupee: $3344$ Rupees.

03 — Explanation

How do I compare prices given in two different currencies to find the better deal?

Convert both prices into the same currency first, then compare directly — you cannot compare raw numbers across two different currencies.

Example: a camera costs $\$ 540 $in the US, or$ €480 $in France. Given the exchange rate$ \ $1 = €0.88$ , which price is cheaper, and by how much (in dollars)?

Convert the US price into Euros to compare fairly: $540 \times 0.88 = €475.20$ .
Compare: $€475.20$ (US price in Euros) versus $€480$ (France price) — the US price is cheaper.
Find the difference in Euros: $480-475.20=€4.80$ .
Convert the difference back to dollars: $4.80 \div 0.88 = \$ 5.45$ (2 d.p.).

Common Slip

comparing $540$ and $480$ directly just because $480<540$ , without realising the two numbers are in different currencies and cannot be compared until converted to the same one.

04 — Explanation

How do I calculate with money in everyday contexts like bills and change?

Money problems often combine several operations you already know — multiplication for unit prices, addition for totals, and subtraction for change — but the answer must always be interpreted and rounded as real currency at the end.

Example: a family buys $3$ meals at $\$ 8.75 $each and$ 2 $drinks at$ \ $2.40$ each, paying with a $\$ 50$ note. Find the change given.

Cost of meals: $3 \times 8.75 = \$ 26.25$.
Cost of drinks: $2 \times 2.40 = \$ 4.80$.
Total bill: $26.25+4.80=\$ 31.05$.
Change: $50-31.05=\$ 18.95$.

Exam Tip

in multi-step money questions, write down each sub-total clearly as you go rather than trying to do the whole calculation in one line on your calculator — it's much easier to spot (and get partial credit for) an error in one step if every stage is recorded separately.

05 — Common mistakes

Common mistakes to avoid

Dividing instead of multiplying (or vice versa) when converting the "wrong way" relative to how the exchange rate is quoted.
Leaving a money answer with only 1 decimal place, e.g. $\$ 38.5 $instead of$ \ $38.50$ .
Rounding an intermediate converted amount before using it in a further calculation step — keep full accuracy until the final answer.