Question

Mr. Morris wishes to purchase an MGB convertible. When he called on his local British-Leyland dealer he was quoted a price of \(£ 3500 .\) Mr. Morris had planned on spending no more than \(\$ 7500\) for the car. a) If the exchange rate is \(£ 1=\$ 2.20\), can he afford the car? b) How low must the exchange rate be in order for Mr. Morris to buy the car?

Short answer

a) No, Mr. Morris cannot afford the convertible at the given exchange rate since \(£3500 * \frac{2.20}{£1} > \$7500\). b) The exchange rate must be equal to or lower than \(\frac{\$7500}{£3500} \approx \$2.14/£1\) for Mr. Morris to buy the car.

Step-by-step solution

Convert the price of the car in British Pounds to US Dollars

To convert the price of the car (in British Pounds) to US Dollars, we'll use the exchange rate provided: £1 = $2.20. The price of the car in British Pounds is £3500. To convert this to US Dollars, we'll multiply the price by the exchange rate: Price in US Dollars = Price in British Pounds * Exchange rate Price in US Dollars = £3500 * $2.20/£1

Compare the price with the budget

Now we'll compare the converted price to Mr. Morris' budget of $7500. If the converted price is less than or equal to his budget, he can afford the car. If the converted price is greater than his budget, he can't afford the car. Price in US Dollars <= Budget £3500 * \(2.20/£1 <= \)7500 #b) Determine the exchange rate at which Mr. Morris can afford the car.#

Set up an equation to find the required exchange rate

We want to find the exchange rate at which Mr. Morris can afford the car. We'll set up an equation based on the conversion: Price in US Dollars = Price in British Pounds * Exchange rate We know that Mr. Morris' budget is $7500: $7500 = £3500 * Exchange rate

Solve for the exchange rate

Now we'll solve for the exchange rate needed for Mr. Morris to buy the car: Exchange rate = $7500 / £3500

Interpret the result

After determining the exchange rate necessary for Mr. Morris to afford the car, compare it to the current exchange rate to provide a final answer. If the necessary exchange rate is lower than the current rate, then at the current rate, he won't be able to afford the car. However, if the necessary rate is equal to or higher than the current rate, Mr. Morris will be able to buy the car.

Key concepts

Currency Conversion

Understanding currency conversion is crucial for international transactions. It's the process of converting one country's currency into another's, a common practice in global business, tourism, and personal finance. For instance, Mr. Morris’s situation involves converting the British Pound (GBP) to the United States Dollar (USD). To carry out the conversion, you need the current exchange rate, which indicates how much one currency is worth in terms of the other. In his case, the exchange rate is given as £1 = \(2.20.

This implies that for every pound Mr. Morris exchanges, he'll receive \)2.20. To find out how much £3500 will equate to in USD, you multiply the amount in pounds by the exchange rate (3500 x 2.20), which is intuitive and can be done using simple arithmetic or an online currency converter. This procedure is not just critical for overseas purchases like Mr. Morris’s car but also for travelers, international investors, and businesses engaged in export and import activities.

Budgeting in Economics

Budgeting is a vital economic skill that involves planning expenses to ensure financial stability and to avoid overspending. In economics, budgeting helps individuals and organizations allocate resources effectively. Mr. Morris had budgeted \(7500 for his car purchase; this represents a financial ceiling he imposed on his transaction.

In practicing good budget management, he should compare the cost of the car after conversion to his preset budget. If the price in USD exceeds \)7500, purchasing the car would break his budget, making it unaffordable. In real-life scenarios, budgeting could involve additional costs such as taxes, insurance, and maintenance, which should be factored into the initial budget. Effective budgeting requires individuals to constantly update their financial plans to reflect changes in income, expenses, and personal economic goals.

Exchange Rate Calculation

An exchange rate calculation is used to determine how much of one currency can be received in exchange for another currency. Exchange rates fluctuate based on market conditions, such as supply and demand, economic indicators, and geopolitical stability. Mr. Morris’s exercise involves reverse-calculating the exchange rate that would make the car affordable within his budget.

To solve part (b) of the given problem, an equation is set up with his budget (\(7500) and the cost in pounds (£3500). By dividing the two amounts, the exchange rate can be found, matching the budget to the price (\)7500 / £3500). This calculation often requires understanding of cross-multiplication and division principles, making it essential for those involved in financial planning and international trade to grasp how exchange rates are determined and how they affect currency conversion and purchasing power.