Originally Posted by
Боб Уайтман
I want to add that declension of compound numerals is complicated in Russian, and many native speakers do not bother to decline them properly. Some less-educated Russians are even unable to.
So, yes, "от восьмисот семидесяти одной тысячи рублей" is the only correct way to read this numerical expression. If it is cited in a TV announcement, they would certainly pronounce it correctly. But if you just hear this expression somewhere in the street, I guess most likely it would sound as "от восемьсот семьдесят одной тысячи рублей" (I underlined the parts which are left undeclined). Although that is considered to be grammatically wrong, a lot of people say that way.
I am not telling that foreigners should learn that way. But at least they need to be aware of that fact, I think.