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Question

Difficulty: MediumForeign Exchange Market, Systems, and Exchange Rate Determination

If the foreign exchange rate of the US Dollar ()againsttheNigerianNaira(₦)changesfrom) against the Nigerian Naira (₦) changes from 1 = ₦400 to $1 = ₦500, what is the percentage depreciation of the Naira against the US Dollar?

Answer: 20 %

Answer

The percentage depreciation of the Naira against the US Dollar is 20%.
Currency depreciation represents the percentage decrease in the value of a domestic currency relative to a foreign currency. Initially, ₦1 bought 1400=\frac{1}{400} = 0.0025 .Aftertheexchangeratechangedto. After the exchange rate changed to 1 = ₦500, ₦1 buys 1500=\frac{1}{500} = 0.0020 .Thelossinvalueis. The loss in value is 0.0005 per Naira, which equals a 20% decline from the initial value of $0.0025.

Step-by-Step Solution

1
Determine the initial value of 1 Naira in terms of US Dollars
Initial value of ₦1 = 1400=\frac{1}{400} = 0.0025$
Currency value is expressed in terms of how many units of foreign currency one unit of domestic currency can buy.
2
Determine the new value of 1 Naira in terms of US Dollars
New value of ₦1 = 1500=\frac{1}{500} = 0.0020$
To assess the new purchasing power of 1 unit of domestic currency in foreign exchange.
3
Calculate the absolute decrease in the value of 1 Naira
Loss in value = 0.0025−0.0020=0.0025 - 0.0020 = 0.0005$
To find the magnitude of the loss in currency value.
4
Compute the percentage depreciation
Percentage depreciation = 0.00050.0025×100%=20%\frac{0.0005}{0.0025} \times 100\% = 20\%
Percentage depreciation measures the change in value relative to the original value of the domestic currency.

Key Concept

Currency Depreciation Calculation
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Topics

Foreign Exchange Market, Systems, and Exchange Rate Determination

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