How is this isopropyl and not propyl (organic chem nomenclature)

I am having trouble understanding the isomers of alkyls, for some reason. My book doesn't explain it well. The chain is below...when I put something in brackets it means it is a substituent on that carbon:

CH3-CH2-CH2- CH [CH2CH3 ]-CH [CH(CH3)2)] -CH2-CH2-CH3

The name is 4-ethyl-5-isopropyloctane. I am tempted to drop the iso in it, since I recognize that substituent as a propyl. Can someone please clear this up for me, and how I can recognize that as an iso-propyl and not just a normal propyl? Thanks!

Any time an alkyl substituent forks at the end (like the shape of the letter Y), and each end of the fork is a methyl group then it is called "iso" something or other. If the alkyl substituent has three carbon atoms and ends in a fork then it is an isopropyl group and we would write it like this CH(CH3)2 because there are two methyl groups, CH3, connected to the first carbon. (if it is simply three carbons all in a strait chain, CH2CH2CH3, then it is just a propyl group). If there are four carbons in the alkyl substituent and it ends with a fork, two carbons in line then a fork with a methyl on either side like this: CH2CH(CH3)2, then we call it isobutyl (if it is simply four carbons all in a strait chain, CH2CH2CH2CH3, then it is just a butyl group). The same is true for pentyl, CH2CH2CH2CH2CH3, and isopentyl, CH2CH2CH(CH3)2.

The group CH(CH3)2 is a methyl group in which two hydrogens have been replaced by two methyl groups. This dimethylmethyl is called isopropyl (or 2-propyl) in order to distinguish it from the straight chain three carbon group which is normal propyl or n-propyl.