Question

exchange rate and purchasing power quick check
if 100 u.s. dollars traded for 150 canadian dollars yesterday, but 150 u.s. dollars trades for 300 canadian dollars today, which of the following is correct? (1 point)
the u.s. dollar depreciated with respect to the canadian dollar, and the canadian dollar depreciated with respect to the u.s. dollar.
the u.s. dollar appreciated with respect to the canadian dollar, and the canadian dollar appreciated with respect to the u.s. dollar.
the u.s. dollar depreciated with respect to the canadian dollar, and the canadian dollar appreciated with respect to the u.s. dollar.
the u.s. dollar appreciated with respect to the canadian dollar, and the canadian dollar depreciated with respect to the u.s. dollar.

Explanation:

Step1: Calculate yesterday's exchange rate

Yesterday, 100 US dollars = 150 Canadian dollars. So, 1 US dollar = \( \frac{150}{100} = 1.5 \) Canadian dollars.

Step2: Calculate today's exchange rate

Today, 150 US dollars = 300 Canadian dollars. So, 1 US dollar = \( \frac{300}{150} = 2 \) Canadian dollars.

Step3: Analyze US dollar's value

Since 1 US dollar can buy more Canadian dollars today (2 vs. 1.5 yesterday), the US dollar appreciated against the Canadian dollar.

Step4: Analyze Canadian dollar's value

To find how many US dollars 1 Canadian dollar can buy:

• Yesterday: 1 Canadian dollar = \( \frac{100}{150} \approx 0.6667 \) US dollars.
• Today: 1 Canadian dollar = \( \frac{150}{300} = 0.5 \) US dollars.

Since 1 Canadian dollar can buy fewer US dollars today, the Canadian dollar depreciated against the US dollar.

Answer:

The U.S. dollar appreciated with respect to the Canadian dollar, and the Canadian dollar depreciated with respect to the U.S. dollar. (The option with this description, e.g., if it's the fourth option, write "D. The U.S. dollar appreciated with respect to the Canadian dollar, and the Canadian dollar depreciated with respect to the U.S. dollar.")