Question

the exchange rate between non-fixed currencies continually fluctuates. the chart below shows the exchange rate of the us dollar to the japanese yen over the course of six days.

\

$$\begin{tabular}{|c|c|} \\hline day & \\$:\\yen \\\\ \\hline monday & 1:88.6122 \\\\ \\hline tuesday & 1:90.8305 \\\\ \\hline wednesday & 1:87.5507 \\\\ \\hline thursday & 1:91.2323 \\\\ \\hline friday & 1:92.7120 \\\\ \\hline saturday & 1:89.4477 \\\\ \\hline \\end{tabular}$$

mary has \\$311.75 to convert into yen. the currency exchange she is using charges a surcharge of 6\\% when converting currency. about how many more yen will mary receive if she makes her trade on the day with the most favorable exchange rate than if she makes her trade on the day with the least favorable exchange rate?
a. \yen 1,125
b. \yen 1,513
c. \yen 1,609
d. \yen 1,706

Explanation:

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<reasoning>

Identify the most and least favorable exchange rates

Using the Currency Exchange Rates knowledge point

• Most favorable rate (highest yen per dollar): Friday at \(1:92.7120\)
• Least favorable rate (lowest yen per dollar): Wednesday at \(1:87.5507\)

Calculate the amount converted after surcharge

Using the Transaction Fees knowledge point
\[

$$\begin{aligned} &\text{Surcharge Rate} = 6\% = 0.06\\ &\text{Amount after surcharge} = \$311.75 \times (1 - 0.06) = \$311.75 \times 0.94 = \$293.045 \end{aligned}$$

\]

Calculate yen received on the most favorable day

Using the Currency Conversion knowledge point
\[
\text{Yen on Friday} = 293.045 \times 92.7120 \approx 27,168.786 \text{ yen}
\]

Calculate yen received on the least favorable day

Using the Currency Conversion knowledge point
\[
\text{Yen on Wednesday} = 293.045 \times 87.5507 \approx 25,656.300 \text{ yen}
\]

Calculate the difference in yen received

Using the Currency Conversion knowledge point
\[

$$\begin{aligned} &\text{Difference} = 27,168.786 - 25,656.300 = 1,512.486 \text{ yen}\\ &\text{Difference} \approx \yen 1,513 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>a. \(\yen 1,125\)</mcq-option>
<mcq-correct>b. \(\yen 1,513\)</mcq-correct>
<mcq-option>c. \(\yen 1,609\)</mcq-option>
<mcq-option>d. \(\yen 1,706\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the most and least favorable exchange rates

Using the Currency Exchange Rates knowledge point

• Most favorable rate (highest yen per dollar): Friday at \(1:92.7120\)
• Least favorable rate (lowest yen per dollar): Wednesday at \(1:87.5507\)

Calculate the amount converted after surcharge

Using the Transaction Fees knowledge point
\[

$$\begin{aligned} &\text{Surcharge Rate} = 6\% = 0.06\\ &\text{Amount after surcharge} = \$311.75 \times (1 - 0.06) = \$311.75 \times 0.94 = \$293.045 \end{aligned}$$

\]

Calculate yen received on the most favorable day

Using the Currency Conversion knowledge point
\[
\text{Yen on Friday} = 293.045 \times 92.7120 \approx 27,168.786 \text{ yen}
\]

Calculate yen received on the least favorable day

Using the Currency Conversion knowledge point
\[
\text{Yen on Wednesday} = 293.045 \times 87.5507 \approx 25,656.300 \text{ yen}
\]

Calculate the difference in yen received

Using the Currency Conversion knowledge point
\[

$$\begin{aligned} &\text{Difference} = 27,168.786 - 25,656.300 = 1,512.486 \text{ yen}\\ &\text{Difference} \approx \yen 1,513 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>a. \(\yen 1,125\)</mcq-option>
<mcq-correct>b. \(\yen 1,513\)</mcq-correct>
<mcq-option>c. \(\yen 1,609\)</mcq-option>
<mcq-option>d. \(\yen 1,706\)</mcq-option>
</answer>

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