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Chapter 1: Problem 27

At the end of 2006 an expert economist from the Global Economic Institute in Kiel, Germany, predicted a drop in the value of the dollar against the euro of \(10 \%\) over the next 5 years. If the exchange rate was \(\$ 1.27\) to 1 euro on November \(5,2006,\) and was \(\$ 1.45\) to 1 euro on November \(5,2007,\) what was the actual drop in the value of the dollar over the first year?

Short Answer

Expert verified
Answer: The difference between the predicted and actual percentage drop in the value of the dollar against the euro after the first year was approximately 14.185%.

Step by step solution

01

1. Find the predicted value of the dollar after one year

According to the economist's prediction, the dollar will drop by \(10 \%\) over 5 years. To find the predicted drop for one year, divide 10 by 5: \(10 \% ÷ 5 = 2 \%\). So the predicted drop in the value of the dollar after one year is \(2 \%\).
02

2. Calculate the predicted future exchange rate

To find the predicted exchange rate after one year, we will use the formula: Future Exchange Rate = Initial Exchange Rate x (1 - Percentage Drop) In this case: Initial Exchange Rate = \(\$1.27\) Percentage Drop = \(2 \% = 0.02\) Calculate the predicted future exchange rate: Future Exchange Rate = \((\$1.27) \times (1 - 0.02) = 1.27 \times 0.98 = \$1.2446\)
03

3. Calculate the actual drop in the value of the dollar

Now, we need to find the actual drop in the value of the dollar by comparing the actual exchange rate to the predicted exchange rate. On November 5, 2007, the exchange rate was \(\$1.45\) to 1 euro. The difference between the predicted rate and the actual rate is: Actual Drop = Actual Exchange Rate - Predicted Exchange Rate = \((\$1.45 - \$1.2446) = \$0.2054\)
04

4. Calculate the percentage of the actual drop

Lastly, we need to find the percentage drop in the value of the dollar. To do this, use the following formula: Percentage Drop = (Actual Drop / Initial Exchange Rate) x 100 In this case: Actual Drop = \(\$0.2054\) Initial Exchange Rate = \(\$1.27\) Calculate the percentage drop: Percentage Drop = \((\$0.2054 / \$1.27) \times 100 = 0.16185 \times 100 = 16.185 \%\) The actual drop in the value of the dollar over the first year was \(16.185 \%\).

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