Limited Time Offer: Save 10% on all 2021 and 2022 Premium Study Packages with promo code: BLOG10    Select your Premium Package »

Percentage Change in a Currency Relative to Another Currency

Percentage Change in a Currency Relative to Another Currency

Calculating Percentage Appreciation/Depreciation

To calculate the percentage change, one needs to clearly understand the base currency and the price currency.  Let’s take the Chinese Yuan (CNY) and South African Rand (ZAR) example. The ZAR/CNY exchange rate increased from 1.6459 to 1.8356. Therefore, the percentage appreciation will be:

$$\frac{1.8356}{1.6459} – 1 = 11.5256\%$$

This represents an 11.5256 percent appreciation in the Chinese Yuan against the South African Rand. The ZAR/CNY exchange rate is expressed with the Chinese Yuan as the base currency and South African Rand as the price currency. In other words, you now need more South African Rands to buy one Chinese Yuan.

Interpretation of the Percentage Appreciation/Depreciation

The appreciation of the Chinese Yuan against the South African Rand can also be expressed as a depreciation of the South African Rand against the Chinese Yuan. However, the depreciation percentage, in this case, will not be equal to the previous appreciation percentage of 11.5256%.

To invert a currency exchange rate, we have to divide 1 by the exchange rate:

If $$\frac{ZAR}{CNY} = 1.6459$$

$$\frac{CNY}{ZAR} = \frac{1}{1.6459} = 0.6076$$

To calculate the depreciation percentage of South African Rand if the exchange rate ZAR/CNY increased from 1.6459 to 1.8356, we have to invert the exchange rate from ZAR/CNY to CNY/ZAR so that the Chinese Yuan becomes the price currency and the South African Rand, the base currency. That is:

$$\frac{\frac{1}{1.8356}}{\frac{1}{1.6459}} – 1 = \frac{0.5448}{0.6076} -1 = -10.3358\%$$

Thus, we can see that the depreciation percentage of the South African Rand is not the same as the Chinese Yuan’s appreciation.

Example: Appreciation/Depreciation With a Forward Rate

A forex trader noticed that the USD/EUR spot rate is 1.2960 and is expected to be 1.2863 after one year (forward rate). Calculate the euro (EUR) expected appreciation/depreciation against the US dollar over the next year.


We know that we are dealing with USD/EUR quotes. So, we calculate as:


This was expected because clearly, there was a decrease in USD/EUR, indicating that EUR is depreciating.


Which of the following best describes a 4% appreciation in the ZAR/CNY exchange rate?

A. This represents a 4 percent appreciation in the South African Rand (ZAR) as compared to the Chinese Yuan.

B. This represents a 4 percent appreciation in the Chinese Yuan (CNY) as compared to the South African Rand.

C. This represents a 4 percent depreciation in the Chinese Yuan (CNY) as compared to the South African Rand.


The correct answer is B.

A 4% appreciation in the ZAR/CNY exchange rate  represents an appreciation of the base currency against the price currency. In this case, the Chinese Yuan appreciates against the South African Rand. Therefore, the appreciation represents a 4 percent increase in Chinese Yuan, relative to the South African Rand.

Featured Study with Us
CFA® Exam and FRM® Exam Prep Platform offered by AnalystPrep

Study Platform

Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Online Tutoring
    Our videos feature professional educators presenting in-depth explanations of all topics introduced in the curriculum.

    Video Lessons

    Sergio Torrico
    Sergio Torrico
    Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
    So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
    Kriti Dhawan
    Kriti Dhawan
    A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
    nikhil kumar
    nikhil kumar
    Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
    Great support throughout the course by the team, did not feel neglected
    Benjamin anonymous
    Benjamin anonymous
    I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
    Daniel Glyn
    Daniel Glyn
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.