The first thing you realize when you learn to read the Cyrillic alphabet is that many of these mysterious Russian words look just like English words. There are many of those, such as funksiya/function, plan/plan, nationalnih/national, etc... 

I counted each "loan word" in the 3000 most frequently used words in Russian. I counted only words that will be transparent to the English speaker. I did not include the "russian words" such as perestroika, pravda, kopeck, etc... I did not include either words that look a bit different but share the same Indo-European words as their English equivalents and thus are quite easy to learn.

This statistic is thus a bare minimum of the words you should more or less immediately understand once you can read Cyrillic.

As you can see, more than 10% of the 3000 most common Russian words are almost immediately intelligible to the English speaker.