Question

The U.S. dollar exchange rate increased from \(\$ 0.96\) Canadian in June 2011 to \(\$ 1.03\) Canadian in June \(2012,\) and it decreased from 81 Japanese yen in June 2011 to 78 yen in June 2012. What was the value of 100 yen in terms of U.S. dollars in June 2011 and June 2012 ? Did the yen appreciate or depreciate against the U.S. dollar over the year June 2011 to June \(2012 ?\)

Short answer

In June 2011, 100 yen was approximately 1.235 dollars, and in June 2012, it was approximately 1.282 dollars. The yen depreciated against the U.S. dollar from June 2011 to June 2012.

Step-by-step solution

- Identify the exchange rates

The value of the U.S. dollar in terms of Canadian dollars and Japanese yen are given. In June 2011, 1 U.S. dollar was equivalent to 81 Japanese yen. In June 2012, 1 U.S. dollar was equivalent to 78 Japanese yen.

- Calculate the value of 100 yen in U.S. dollars for June 2011

To find the value of 100 yen in terms of U.S. dollars for June 2011, we need to calculate \( \frac{100 \text{ yen}}{81 \text{ yen/dollar}} \) which gives \( \frac{100}{81} \approx 1.235 \text{ dollars} \).

- Calculate the value of 100 yen in U.S. dollars for June 2012

To find the value of 100 yen in terms of U.S. dollars for June 2012, we need to calculate \( \frac{100 \text{ yen}}{78 \text{ yen/dollar}} \) which gives \( \frac{100}{78} \approx 1.282 \text{ dollars} \).

- Determine appreciation or depreciation

To determine whether the yen appreciated or depreciated against the U.S. dollar, we compare the values of 100 yen in June 2011 and June 2012. Since the value of 100 yen increased from 1.235 dollars to 1.282 dollars, the yen depreciated against the U.S. dollar.

Key concepts

currency depreciation

Currency depreciation refers to a decrease in the value of one currency relative to another. For example, if 1 U.S. dollar could buy 81 Japanese yen in June 2011 but buys 78 yen in June 2012, it indicates that the yen has depreciated relative to the dollar. This is because it now takes more yen to buy the same amount of dollars.

Depreciation can result from various factors including economic instability, inflation, and reduced demand for the currency.

currency appreciation

Currency appreciation is the increase in value of one currency relative to another. If the value of 1 U.S. dollar decreases from 81 yen to 78 yen between June 2011 and June 2012, this indicates that the U.S. dollar appreciated against the yen. This is reflected in the fact that fewer yen are needed to buy 1 dollar now as compared to before.

Appreciation can be triggered by strong economic indicators, higher demand for the currency, or favorable trading conditions.

foreign exchange market

The foreign exchange market, or forex market, is where currencies are traded. It is a global, decentralized market that determines exchange rates for every currency. The forex market is crucial for international trade, as it allows businesses to convert one currency to another and conduct transactions across countries.

Forex market participants include banks, corporations, governments, and retail traders. The market operates 24/7 and is influenced by economic data, geopolitical events, and market speculation.

currency conversion

Currency conversion is the process of exchanging one currency for another. For instance, if you want to convert 100 Japanese yen to U.S. dollars in June 2011, you use the exchange rate of 81 yen per dollar. Hence, \( \frac{100 \text{ yen}}{81 \text{ yen/dollar}} ≈ 1.235 \text{ dollars} \).

Similarly, to convert 100 yen in June 2012 using an exchange rate of 78 yen per dollar, you calculate \( \frac{100 \text{ yen}}{78 \text{ yen/dollar}} ≈ 1.282 \text{ dollars} \). Currency conversion is essential for travelers, businesses, and investors dealing in different currencies.