How Do We Convert Currencies and Measure Exchange-Rate Changes?
At 0.80 EUR per USD, one US dollar buys 0.80 euros. To convert dollars to euros, multiply the dollar amount by euros per dollar. A payment of USD 250 becomes EUR 200. To convert euros to dollars, divide by 0.80: EUR 200 buys USD 250 before fees.
Builds on: What Is an Exchange Rate?
What you will learn
- Write the rate's units before multiplying or dividing.
- Calculate conversions with units
- Explain appreciation and depreciation
Essential definitions
- Exchange rate
- The price of one currency expressed in another currency.
- Appreciation
- An increase in a currency’s value under a floating exchange-rate system.
- Depreciation
- A decrease in a currency’s value under a floating exchange-rate system.
Let the units determine the calculation
At 0.80 EUR per USD, one US dollar buys 0.80 euros. To convert dollars to euros, multiply the dollar amount by euros per dollar. A payment of USD 250 becomes EUR 200. To convert euros to dollars, divide by 0.80: EUR 200 buys USD 250 before fees.
The reciprocal quote is 1 ÷ 0.80 = 1.25 USD per EUR. Both describe the same opportunity. A nominal unit buying many units of another currency does not by itself show economic strength; currency unit sizes are conventions.
Calculate and interpret a change
Percentage change = (new quote − original quote) ÷ original quote × 100. Both quotes must use the same direction and units. A rise from 0.80 to 0.88 EUR per USD is 10%. Each dollar buys more euros, so the dollar appreciates.
The reciprocal falls from 1.25 to about 1.1364 USD per EUR, a fall of about 9.09%, not 10%. Each percentage uses a different original denominator. If a US exporter keeps its price at USD 100, the European buyer's price rises from EUR 80 to EUR 88, potentially weakening demand. State that the contract price is unchanged. Fees, different buying and selling rates, hedging and firms changing margins can alter actual payments or delay pass-through.
Hypothetical conversion and reciprocal
- Exchange rate = 0.80 EUR per USD. A payment of 250 USD costs 250 × 0.80 = 200 EUR.
- A budget of 200 EUR buys 200 ÷ 0.80 = 250 USD, ignoring fees.
- If the rate rises to 0.88, the dollar appreciation is (0.88 − 0.80) ÷ 0.80 × 100 = 10%.
The quote’s units determine whether to multiply or divide and which currency appreciates.
Apply and evaluate
- Exchange fees, contract currency and delayed pass-through can change the final buyer price.
- Nominal currency-unit comparisons are not a measure of purchasing power or national living standards.
Common misconceptions
- A numerically higher rate does not identify appreciation until the quote direction is stated.
- A 10% appreciation of one currency does not imply exactly a 10% depreciation of its reciprocal.
Knowledge check
At 0.80 EUR per USD, how many dollars buy one euro?
What to remember
Write the rate's units before multiplying or dividing. Percentage changes depend on the original quote, so a currency's rise and its partner's fall need not have equal percentages.
Completion records your reflection, not a test score.
Lessons in this section
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