Question

Marcellus is traveling abroad in Ghana and using traveler's checks, which he has acquired from Easy Traveler's Savings Bank. Easy Traveler's Savings Bank charges a 7\% fee on traveler's checks, which can then be used like cash at any location overseas at the same exchange rate, and any change will then be returned to Marcellus in local currency. For this trip, Marcellus bought a 651 Cedi traveler's check and paid a fee of \(32.30\) USD (United States dollars) for the check.

Short answer

Marcellus paid approximately \(493.73\) USD for the 651 Cedi traveler's check, including the fee.

Step-by-step solution

Calculate cost without the fee

In this step, let's find out how much the 651 Cedi traveler's check costs in USD without the fee. To do this, we'll use this equation: \(Cost_{before\_fee} = \frac{Fee}{(Fee\_Rate / 100)}\) Where: - \(Cost_{before\_fee}\) is the traveler's check cost without the fee - \(Fee\) is the known fee paid by Marcellus = $32.30. - \(Fee\_Rate\) is the fee rate = 7\%. Plugging in the values from the problem, we have: \(Cost_{before\_fee} = \frac{32.30}{(7 / 100)}\) Calculating the cost without the fee, we get: \(Cost_{before\_fee} = 32.30 / 0.07 \approx 461.43\) USD.

Calculate total cost, including the fee

Now, let's calculate the total cost of the traveler's check, including the fee. We do that by adding the computed cost without the fee to the known fee. \(Cost_{total} = Cost_{before\_fee} + Fee\) We know the following values: - \(Cost_{before\_fee} \approx 461.43\) USD - \(Fee = 32.30\) USD Plugging in the values, we get: \(Cost_{total} = 461.43 + 32.30 = 493.73\) USD. So, Marcellus paid approximately \(493.73\) USD for the 651 Cedi traveler's check, including the fee.

Key concepts

Traveler's Checks Mathematics

Traveler's checks serve as a safer alternative to carrying cash, especially when traveling abroad. When dealing with traveler's checks mathematics, one needs to understand the basics of how fees are calculated and how these checks operate within the context of currency exchange.

For example, in the given exercise, Marcellus's experience with acquiring Ghanaian Cedi via traveler's checks provides a practical scenario. The mathematics behind these transactions involves calculating the value of the foreign currency that can be obtained after accounting for service fees. These fees are usually a fixed percentage of the total amount of the check. To accurately determine the value Marcellus receives after fees, one first calculates the cost of the check without the fee and then adds the fee to find the total cost. What this means is that understanding percentage and basic algebra is crucial in traveler's checks mathematics.

Additionally, the ease with traveler's checks are accepted and exchanged abroad relies on their fixed exchange rates, meaning the user doesn't have to grapple with fluctuating currency values at the time of the transaction.

Currency Conversion Calculation

Currency conversion is essential when traveling internationally or when dealing with financial transactions across borders. The process of currency conversion calculation involves the conversion of one type of currency into another at a specific conversion rate.

This rate might be set by financial markets or specific institutions issuing traveler's checks or currency exchange services. It's crucial to know the current exchange rate to calculate the equivalent amount in the new currency. This involves multiplying the amount in the original currency by the exchange rate.

In our exercise, although the exact exchange rate is not provided, it can be inferred through the calculations. The total cost in US dollars that Marcellus paid for the Cedi traveler's check helps to understand the effective exchange rate used by Easy Traveler's Savings Bank, which is inclusive of the 7% fee. Hence, the value of 1 Cedi in terms of US dollars can be deduced if one integrates the cost information given in the exercise.

Percentage Fee Calculation

When receiving or exchanging money, particularly in traveler's checks, understanding percentage fee calculation is vital. This fee is a portion of the total amount and is calculated as a percentage. To figure out the fee alone, one can multiply the total amount before the fee by the percentage rate.

Conversely, if only the fee is known, as in Marcellus's case, and one needs to find the original amount before the fee was applied, the calculation is different. You would divide the fee by the percentage rate (in decimal form). This calculation was demonstrated in the exercise when finding out the cost of the traveler's check without the service fee.

Understanding how to calculate percentage fees is a useful skill not only for traveler's checks but also for other financial services such as loans, investments, and credit card transactions. Being skilled in percentage calculations allows individuals to make informed financial decisions and understand how much they are truly paying in fees.