Effectively most subs around $100 pretty much stink.
HTIB subs from Sony, Onkyo, etc - are especially horrible.
If your budget is truly $100 you'd better look for a half price sale, or perhaps something used off craigslist or even this forum.
Wharfedales are not a bad set of speakers. You could do MUCH worse. I own Wharfedale Sapphire towers, including a pair of Sapphire bookshelves and like them. They'll sure outclass a $100 sub.
To give you an idea of why I'm not too excited about budget subs - take a look at this Pioneer SW-8 frequency response graphing I performed. Read the review - digest it. Realize how much of an utter failure this sub is compared to subs that cost $200 or $300. Yes it's double or triple the price - but it's way way way more than 2 or 3x's the performance. And we aren't talking big money here - we are talking about saving for another week or maybe even a month if you are younger --- It's worth the wait!
Keep in mind that the SW-8 sub that reviewed so poorly is a 5 star out of 5 star rating on newegg. I guess people just don't know or care. it's definitely an audible thing - it's not like you can't tell if you listen. Just depends on how much you like listening to music and watching movies on something that sounds good.
The non discerning purchaser hears lower sound and says --- yep this set out to do exactly what I wanted it to do - adds rumble. The majority of folk on this forum would most likely NOT be happy with the SW-8. I'd personally rate it about a 1 star -- 2 if I was feeling generous. I have one - I actually RMA'ed the first one because it was so bad I thought it was broken. Sad thing is - the SW-8 is significantly better than most HTIB subwoofers. A buddy of mine bought a Polk PSW10 on one of the recent sales for $80. If you haven't heard better it's great --- that's what he said to me. My response - Once you've heard better then it sounds like it's farting on nearly every note.
I personally wouldn't recommend much under $300, and then I'd recommend the Klipsch RW-12D from what I know currently to be available. That's way over your stated budget - and if you don't need that much to be happy - then ignore --- but in my mind that's about the cheapest budget sub I've heard that would be satisfactory to me. If you trust the newegg reviewers than the SW-8 is all the rave.
The BIC F12 at $199 is so much a better sub than the SW-8 that any comparison is utterly pointless. The SW-8 taxes out at about 85dB max. The BIC F12 at about 115dB. Both falter a bit above 30hz, but you could actually enjoy watching a movie with the BIC F12. The RW-12D I mentioned earlier covers the majority of the subwoofer audible frequency spectrum for the most part and is a better subwoofer for that reason --- extending to down to 22hz or 24hz or so which is pretty outstanding at the $300 pricepoint.
This thread might be a reasonable resource to you to see what others recommend at pricepoints: I've come to realize I'm a bit of a spoiled subwoofer snob these days - but once you hear a good sub - it's hard to go back and get any excitement boiled up about inexpensive offerings.