General percentage change question help!
A company imports components and pays in Euros. On a particular day in 2011; they found that the price of one component, in euros, was 10% less than it was when they bought it in 2009.
The exchange rate had also changed over two years in reference to when they completed the transaction in 2009:
a, 2009, 1E=£1
b, 2010, 1E = £0.95
c, 2011, 1E = £0.90
Find a percentage change in £ of the component in question between day a in 2009 and day c in 2011
Right, there is obviously a 10% deduction in the exchange rate over the two years, but really struggling how to incorporate this into the initial price deduction?! Would it involve using P = M(1-r%)^n ?
Any help would be greatly appreciated!
Re: General percentage change question help!
If I understand the problem correctly, it isn't as hard as it appears.
Let the price of the Item be P, in in the year 2009. P E = P £ in 2009
Then the price of the Item, in Euros, in the year 2011, is (.90)P
As you've noted, the decrease in terms of exchange is 10%, so the P in 2011 converted into pounds is (.90)(.90)P = (.81)P
In summary, the price of the item went from P£ to (.81)P £. Hence the net decrease (in terms of £) is 19%