How To Change Base currency for a multi store site

I will paraphrase the answer of St0iK. You can't set different base currency per store, but you can do it per website. First you have to go to the admin panel -> System -> Configuration -> CATALOG -> Catalog -> Price -> Catalog Price Scope and change it from Global to Website. Now when you go to the admin panel -> System -> Configuration -> GENERAL -> Currency Setup -> Currency Options you can change Base Currency per Website, not only for Default (Global). So you have to transfer you stores to websites and you will be able to do what you want.

It turns out that Base Currency can be set on each Store View. However, this option was not presented on the admin side. I had to change the system.xml

app/code/core/Mage/Directory/etc/system.xml

<label>Base Currency</label>

I have to set the appropriate to change from 0 to 1

<show_in_store>1</show_in_store>

Once this was done, I could see Base Currency under "Currency Options" even within a store view. This now works well and everything seems to be working fine.

You need to set-up multiple websites, one for each currency (not just store views, complete websites)

Then you will be able to change the store from the Configuration scope dropdown in settings, and un-check the checkbox(Use website) on the currency.

Then you will be able to set different currencies for each of your stores.