Question

The Euro appreciates 5% versus the yen. The Peso depreciates 5% versus the Euro. What is the approximate appreciation or depreciation of the Yen/Peso exchange rate?

Answer 1

Answer>

Let x Euros can be bought by 1 Yen

Let y Pesos can be bought by 1 Euro

Let z Yens can be bought by 1 Peso

Now, The new Euro/yen exchange rate = 1.05x per yen

New Peso/Euro exchange rate = 0.95y per Euro

Also, we can approximate z as,

z = 1/x * 1/y = 1/xy

So approximate change in z when the new rates apply

z' = 1/(1.05x * 0.95y)

z' = 1/(0.9975xy)

so the change in new vs old exchange rate of Yen/Peso = z' / z

= 1/(0.9975) * (xy/xy)

= 1/0.9975

= 1.0025. Therefore percentage increase = 1.0025 - 1 = 0.0025 = 0.25%

Hence, The Yen/Peso exchange rate appreciates by 0.25% approximately.

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