## 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