Another point on this, which I really saw in action on a recent project - a "big" n is probably much bigger than you think. Sometimes it can be easy to think "oh, this is going to have to do 100,000 operations, I definitely need to optimize it" - but computers are fast, and 100,000 multiplications (for example) happens so fast you probably don't need to think too hard about it.
That's not to say you shouldn't think at all, just that it's often surprising how insanely fast modern computing hardware is.