The exchange rate between non-fixed currencies continuously fluctuates. The table below shows the exchange rate of the US dollar to the euro over the course of six days.
| Day | $: \epsilon |
| -------- | ----------- |
| Monday | $1: 0.7102$ |
| Tuesday | $1: 0.7544$ |
| Wednesday| $1: 0.7053$ |
| Thursday | $1: 0.6910$ |
| Friday | $1: 0.6869$ |
| Saturday | $1: 0.7273$ |
Sandy has $829.04 to convert into euros. How many more euros would Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate? Round all currencies to two decimal places.
a. € 33.49
b. € 55.96
c. € 67.04
Answer (2)
Sandy would have €56.24 more if she exchanged her dollars on the day with the most favorable rate compared to the least favorable rate. The calculations show that exchanging on Tuesday results in €625.42, while Friday’s exchange yields €569.18. Thus, the difference is €56.24.
;
Identify the most favorable (0.7544) and least favorable (0.6869) exchange rates.
Calculate euros at the most favorable rate: $829.04 × 0.7544 = 625.42 .
Calculate euros at the least favorable rate: $829.04 × 0.6869 = 569.18 .
Find the difference: 625.42 − 569.18 = 56.24 .
Explanation
Problem Analysis Sandy has $829.04 to convert into euros. We need to find the difference in the amount of euros she would have if she converted her money on the day with the most favorable exchange rate compared to the day with the least favorable exchange rate.
Identify Extreme Exchange Rates First, we need to identify the most and least favorable exchange rates from the given table. The exchange rates are the values in the second column of the table. The most favorable rate is the highest value, and the least favorable rate is the lowest value. From the table, the most favorable rate is 0.7544 and the least favorable rate is 0.6869 .
Calculate Euros at Most Favorable Rate Next, we calculate how many euros Sandy would have if she converted her $829.04 at the most favorable rate. To do this, we multiply the amount of dollars by the most favorable exchange rate: Euros max = $829.04 × 0.7544 = 625.42 So, Sandy would have 625.42 euros if she converted her money on the day with the most favorable exchange rate.
Calculate Euros at Least Favorable Rate Now, we calculate how many euros Sandy would have if she converted her $829.04 at the least favorable rate. To do this, we multiply the amount of dollars by the least favorable exchange rate: Euros min = $829.04 × 0.6869 = 569.18 So, Sandy would have 569.18 euros if she converted her money on the day with the least favorable exchange rate.
Calculate the Difference Finally, we calculate the difference in the amount of euros Sandy would have between the two scenarios. To do this, we subtract the amount of euros she would have at the least favorable rate from the amount of euros she would have at the most favorable rate: Difference = 625.42 − 569.18 = 56.24 Therefore, Sandy would have 56.24 more euros if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate.
Final Answer The difference in euros is 56.24 .
Examples
Understanding exchange rates and their fluctuations is crucial in international finance and trade. For example, imagine a company that imports goods from Europe and pays in euros. If the euro strengthens against the dollar, the company will need to spend more dollars to buy the same amount of euros, increasing their costs. Conversely, if the euro weakens, the company's costs will decrease. By monitoring exchange rates and making informed decisions about when to convert currency, businesses can manage their expenses and maximize their profits. Similarly, individuals traveling abroad can save money by exchanging currency when the exchange rate is favorable.
