CFA Level I Exam · Exchange Rate Calculations

How to Calculate Percentage Change in Currency Value

Updated 7 October 2026 · Fact-checked

Percentage change in a currency's value is measured against another currency using the quote. For a quote P/B (price currency per one unit of base currency), the base currency's percentage change is (new ÷ old) − 1. The price currency's change is (old ÷ new) − 1. The two percentages are not equal and opposite.

Understand Percentage Change in Currency Value

An exchange rate is a price. A quote of USD/EUR = 1.10 means 1 EUR costs 1.10 USD. The currency in the denominator, EUR, is the base currency. The currency in the numerator, USD, is the price currency. The quote tells you how many units of price currency buy one unit of base currency.

If the quote rises, the base currency buys more price currency. So the base currency has appreciated and the price currency has depreciated. If the quote falls, the reverse is true. Direction is easy. The size of the percentage is where marks are lost.

The percentage change in the base currency is simply the percentage change in the quote: (new quote ÷ old quote) − 1. That is because the quote is the price of the base currency, and a price change is measured on the old price.

The price currency is measured on a different footing. Its value in base currency terms is the inverse of the quote, so its change is (old quote ÷ new quote) − 1. Because the starting points differ, the two percentages differ. If one currency appreciates 25%, the other depreciates 20%, not 25%. Always ask: which currency's value am I measuring, and is it the base in this quote?

Key formulas to remember

Quote convention: Quote = price currency / base currency (P/B); Read USD/EUR = 1.10 as 1 EUR = 1.10 USD. EUR is the base.
Change in base currency: % change in base = (S_new ÷ S_old) − 1; Positive means the base appreciated against the price currency.
Change in price currency: % change in price currency = (S_old ÷ S_new) − 1; Equivalent to −(% change in base) ÷ (1 + % change in base).
Inverting a quote: B/P = 1 ÷ (P/B); Use this to restate the quote so the currency you are measuring is the base.

How to solve Percentage Change in Currency Value questions

Use this method for any question asking how much a currency appreciated or depreciated.

1Write the quote as P/B and identify the base currency and the price currency.
2Identify which currency the question asks about.
3If that currency is the base, keep the quote. If not, invert the quote at both dates so it becomes the base.
4Compute (new quote ÷ old quote) − 1 using the quote where your currency is the base.
5Read the sign: positive means appreciation, negative means depreciation.
6Sanity check: the other currency moves in the opposite direction, with a different percentage.
7Pick the option with the right sign and size; the two wrong options often show the inverse-base answer or the sign flipped.

Quickest way: Put the target currency in the base position

When to use it: Any time the question asks about the percentage change of one named currency.

Check whether the named currency is in the denominator of the quote. If yes, compute new ÷ old − 1.
If not, compute old ÷ new − 1 instead. This is the same as inverting first.
Check the sign against direction: did the quote rise or fall?
On the calculator, enter new, divide by old, subtract 1. Example: 1.25 ÷ 1.00 − 1 = 0.25.

Common mistakes in Percentage Change in Currency Value

Reporting the same percentage, with opposite sign, for both currencies.
It feels symmetric: one goes up, the other goes down by the same amount.
Fix: Percentages use different starting values. Recompute using the inverted quote or the old ÷ new formula.
Reading the quote backwards and picking the wrong base currency.
Candidates read USD/EUR as dollars per euro only sometimes, or confuse it with 'USD to EUR'.
Fix: Always read P/B as price currency per one unit of base. The denominator is the base.
Calling a rising quote an appreciation of the price currency.
A bigger number feels like a stronger currency.
Fix: A rising P/B quote means the base currency buys more, so the base appreciated.
Dividing by the new quote instead of the old quote.
Mixing up which value is the starting point.
Fix: A percentage change is always measured relative to the starting value in the same quote.
Inverting only one of the two quotes before computing.
Rushing and inverting just the new rate.
Fix: If you invert, invert both the old and the new quotes, or use the old ÷ new formula.

Worked examples

Example 1

The USD/EUR spot rate moves from 1.2500 to 1.1000. What is the percentage change in the value of the euro relative to the dollar, to the nearest 0.1%? Options: A) −13.6%, B) −12.0%, C) +13.6%.

Show the solution

USD/EUR is price currency USD per 1 base EUR. The euro is the base.
Base change = new ÷ old − 1 = 1.1000 ÷ 1.2500 − 1.
1.1000 ÷ 1.2500 = 0.88, so the change is −0.12 = −12.0%.
The euro depreciated by 12.0%.
Why the other options are wrong: C (+13.6%) is the dollar's change, old ÷ new − 1 = 1.2500 ÷ 1.1000 − 1, so it measures the wrong currency. A (−13.6%) applies old ÷ new to the euro and then flips the sign.

Answer: B) −12.0%. The euro depreciated 12.0% against the dollar.

Example 2

The USD/EUR spot rate moves from 1.2500 to 1.1000. What is the percentage change in the value of the dollar relative to the euro, to the nearest 0.1%? Options: A) −12.0%, B) +12.0%, C) +13.6%.

Show the solution

The dollar is the price currency, so use old ÷ new − 1.
1.2500 ÷ 1.1000 = 1.13636.
Change = 1.13636 − 1 = +0.13636 = +13.6%.
Check by inverting: EUR/USD goes from 0.8000 to 0.9091. New ÷ old = 1.13636, so +13.6%, same result.
The euro fell 12.0% while the dollar rose 13.6%. They are not equal and opposite.
Why the other options are wrong: A (−12.0%) is the euro's change, so it measures the wrong currency. B (+12.0%) is the euro's change with the sign flipped.

Answer: C) +13.6%. The dollar appreciated 13.6% against the euro.

Exam tips

Before computing, circle the currency the question asks about. Then check whether it is the base in the quote.
Options are listed smallest to largest. A sign check removes any option with the wrong sign, but it may leave two options with the same sign, as in example 1 where two options are negative. Then separate them by checking which currency is the base: the base currency's change is new ÷ old − 1, and the price currency's change is old ÷ new − 1.
Expect the same quote movement to be asked from both currencies' point of view in separate questions.
Do not round the quote early. Keep at least four decimals, since the option values can be close.
With no penalty for wrong answers, never leave an item blank, but a quick sign check usually gets you to one of two options.

Practice questions from Exchange Rate Calculations

Percentage Change in Currency Value: frequently asked questions

How do I calculate currency appreciation percentage in CFA Level I?

Put the currency you are measuring in the base position of the quote. Then compute new quote ÷ old quote − 1. A positive result is appreciation and a negative result is depreciation.

Why is the appreciation of one currency not equal to the depreciation of the other?

Each percentage is measured from a different starting value. A move from 1.00 to 1.25 is +25% for the base, but the price currency goes from 1.00 to 0.80 in inverted terms, which is −20%.

Which currency is the base in a quote like USD/EUR?

The euro is the base, because it is in the denominator. The quote shows how many dollars one euro costs.

If the quote rises, which currency has appreciated?

The base currency has appreciated, because one unit of it now buys more of the price currency. The price currency has depreciated.