Hey all just a two part question i am unfamiliar with, if you could show the wor

Question

Hey all just a two part question i am unfamiliar with, if you could show the work and explain how to attain the correct answer and the answer i will award the points

1. Suppose that the US dollar was selling at yen75/$ three years ago. The U.S. dollar is currently selling at yen102/$.   U.S. and Japan had had an inflation of 4.2% and 0.8% for the last three years.

1. How much of the currency rate change was due to the two countries' inflation?

2. How much of the currency rate change was due to other factors than inflation?

Explanation / Answer

1. According to the relative Purchasing Power Parity analysis:

S1/S0 = ((1+I(Japan))/(1+I(US)))^n, where

S1: spot exchange rate 3 years later if only inflation created a change in interest rate

S0: initial exchange rate

I(Japan) = inflation in Japan

I(US) = inflation in US

n = number of years

Hence, S1 = S0 * ((1+I(Japan))/(1+I(US)))^n = 75 * ((1+0.008)/(1+0.042))^3 = Yen 67.90 / $

However, the actual currency change was Yen 102/$ - Yen 75/$ = Yen 27/$

Hence, currency rate change due to inflation = Yen 67.90 / $ - Yen 75/$ = - Yen 7.1 /$

(in % terms ) - Yen 7.1 /$ / Yen 27/$ = -26.31%

2. Change in currency rate = Change due to inflation + Change due to other factors

=> Change due to other factors = Change in currency rate - Change due to inflation

= Yen 27/$ - ( - Yen 7.1 /$) = Yen 34.1 /$

(in % terms ) Yen 34.1 /$ / Yen 27/$ = 126.31%

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