1.5.3 - Exchange rate calculations

Reading a currency quote

An exchange-rate quote states how much of one currency is exchanged for a stated amount of another at a particular time.

In an illustrative October quote, one British pound (GBP) buys 1.25 US dollars (USD). Write this as GBP 1 = USD 1.25. The quote is USD per GBP: each pound corresponds to 1.25 dollars. It does not say that one dollar buys 1.25 pounds. Names and currency codes prevent confusion between different countries' dollars or pounds.

Always identify the starting currency, the required currency and the quote's direction. With this October rate, a GBP 10 price is worth USD 12.50. Going in the reverse direction, USD 10 is worth GBP 8. The different numerical amounts reflect different units, not a gain or loss by themselves.

Actual conversion charges or different buying/selling rates may change the amount received. In the illustrative calculations in this lesson, use the supplied rate and assume no fees unless the question states otherwise. Do not look up a current rate to replace a question's given rate.

Multiplying and dividing

Conversion follows the units in the quote, so multiplication and division are two directions of the same relationship.

For the illustrative October quote GBP 1 = USD 1.25:

An illustrative UK craft business prices a product at GBP 48. At this rate, its dollar equivalent is $48 \times 1.25 = 60$, or USD 60. An illustrative UK retailer receiving an invoice for USD 375 converts back by $375 \div 1.25 = 300$, or GBP 300.

The inverse quote is GBP 0.80 per USD because $1 \div 1.25 = 0.80$. Multiplying USD 375 by 0.80 gives the same GBP 300. Use a single consistent direction; do not divide by 0.80 when converting USD to GBP.

A useful check is to convert the answer back. GBP 300 multiplied by 1.25 gives USD 375. Numerical amounts do not always become smaller in the target currency: that depends on the quoted rate. The reliable rule is the relationship between units, not “always multiply for foreign currency”.

Complete transactions and checks

A business must convert the value of the whole transaction, using consistent quantities, currency and time.

Suppose an illustrative Spanish shop buys 40 bags from a UK supplier in December. Each bag costs GBP 18, and the December quote is EUR 1 = GBP 0.90, with no fees. First calculate the complete invoice in pounds: $40 \times 18 = 720$, or GBP 720. Then convert to euros: $720 \div 0.90 = 800$, or EUR 800.

The alternative route is to convert the unit price first: $18 \div 0.90 = 20$, or EUR 20 per bag, then multiply by 40. Both routes give EUR 800. Converting only GBP 18 would answer the price of one bag rather than the invoice. Do not multiply by the quantity twice.

Keep full precision during intermediate steps, then round the final answer to the precision asked for. For an illustrative January quote EUR 1 = GBP 0.84, a GBP 53 invoice becomes $53 \div 0.84 = 63.095238\ldots$, so its value to two decimal places is EUR 63.10. Rounding the inverse rate early can change the answer.

Use the quote for the relevant transaction date. If a comparison supplies two dates, convert the same stated invoice separately at each rate before comparing. A foreign-currency invoice is not the same as the home-currency amount needed to pay it. Show the substitution and final currency to make the method clear, while recognising that an ordinary correct numerical result can earn full calculation credit without written working.