Wednesday, November 5, 2014

Percentage Change in Ratios Illustrated With Exchange Rate




Question:    The current yen-dollar exchange rate is around 114.    What is the new yen-dollar exchange rate if this exchange rate increases by 10 percent?   What was the dollar-yen exchange rate when the yen-dollar exchange rate was 114?   What is then new dollar-yen exchange rate after the yen-dollar exchange rate increases by 10 percent?


What is the relationship between the percentage change in the yen dollar exchange rate and the dollar-yen exchange rate?  

Answer:  The calculations requested in this problem are summarized in the table below.



Percentage Change in Ratios   -- Illustrated Through Exchange Rates
Current Exchange Rate Yen per dollar
114
Current Exchange Rate Dollar Per Yen
0.00877193
Factor increasing yen/Dollar Rate
1.1
New Yen-Dollar Rate
125.4
New Dollar Yen Rate
0.007974482
Factor Increasing Dollar/Yen Rate
0.909090909
Reciprocal of Factor Impacting Yen/Dollar Rate
0.909090909
% Change in Yen Dollar Rate
0.1
% Change in Dollar Yen Rate
-0.090909091


Observations:

 A ten percent change in the yen/dollar rate is the same as multiplying the dollar yen rate by 1/1.10 or 0.90909.


A ten percentage point increase in the yen/dollar rate is the same as a 9.0909 percentage point decrease in the dollar-yen rate.

I am also teaching exchange rate math at fraction tips:

Exchange rate math problems at fraction tips:
http://fractiontips.blogspot.com/2014/11/exchange-rate-math-post-one.html

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