Mathematics/Currency Value/Accounting Question: help needed

[Up2Late]

I was never good at math, but I know how to do Percentages. I'm have an argument with someone over how much "Real Value" the Dollar has lost over the last 4 years as compared to the value of the Euro.
Here is what I've posted:

Subject:30-35% loss?! Try 65-70%

Message: The Euro hit $0.82 to the Dollar, on October 26, 2000 (Selection day was November 7, 2000). Then the European Central Bank tried to prop up the Euro, but it started to fall again, just before the selection, and it's (the U.S. Dollar) been on a fairly steady fall, ever since...
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Reply-Subject: I was only looking back about two years.

Reply-Message:...But OK, call it $1.30 now. You have $1.30 - $.82 = $.48.

And 130/82 = 1.59, so the Euro has appreciated 59% relative to the
dollar, and the dollar is worth 1/1.59 = .63 = 63% of what it was
then, relative to the Euro, so it has lost 37% of it's value.

If you look back two years, the Euro had gone from around a dollar to
around $1.30, so it's appreciated around 30% relatively speaking. That
is the number I was thinking of. That would give 1/1.30 or a 23% loss
for the dollar.:shrug:


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My Reply-Subject: I under stood where you got the 30%, but on the 4 yr #, you're not ...

My Reply-Subject: ...doing the math correctly.

$.82 x .60 (60%)=0.492
$0.49 + $0.82 =$1.31

Euro peaked (so far) at $1.36

$0.82 x .66 (66%) = 0.5412

$0.54 + $0.82 = $1.36

I wasn't very good at Math, but I'm pretty sure that's how you figure Percentages.
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His Reply-Subject: That's the "1.59" part.

His Reply-Message: The Euro has gone up about 60%. The decline in value of the US$ is the inverse of that. The percentage decrease of the dollar is not that same as the percentage increase of the Euro.
They are inverse to each other.

If the Euro is worth $.82, the dollar is worth 1/.82 = 1.22 Euros.
If the Euro is worth $1.30, the dollar is worth 1/1.30 = .77 Euros.
.77/1.22 = .63 or 63%, so it's lost 37% of it's value relative to the
Euro (100% - 63%).:shrug:

The inverse of .63 is 1.59, which is the number you have.


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So, Who's right? I'm not confident enough in my understanding of Currency Markets to know if I'm right or wrong? Does the last part of what he is doing (starts with "If the Euro is worth $.82...") make any scents? Or is that just some sort of Accounting trick? :shrug:

[unblock]

1. if one currency has doubled in value, the other has lost half its value

so, the euro is now worth 160% relative to the original dollar, then the dollar is now worth 100%/160% = 62.5% relative to the original euro, i.e., a decline of 37.5%.