How Much Will Closing the Teeth Gaps with Invisalign Cost?

Thanks for the picture!! that really helps.
#1- You might not be old enough. I can't tell from the photo, but you look quite young. If you're not, take that as a compliment :-). Invisalign has age requirements.
#2- If I were you I would discuss with your cosmetic dentist options for a) closing the space 2) doing two veneers on your lateral teeth (teeth right next to). This will really create nice proportions for entire smile.
You might be able to do Invisalign Express. Which is about 1/2 price of full Invisalign. Also speak with your dentist. I'd be able to close this using a series of retainers for much less than Invisalign's fee.

In most cases, Invisalign treatment is
comparable to the cost of traditional braces. However, as with other medical
treatments, only your orthodontist can determine the cost, based on your
specific needs. Other factors may include your treatment goals, the difficulty
of your case, how long you are in treatment, and where you live.

Your Orthodontic consultation will be complimentary. The orthodontist will be taking about 8-10 picture and some X rays to extensively evaluate the problem and come up with a good treatment plan. As mentiond this appointment is complimentary at most of the orthodontic offices.
The treatment fees depends upon the severeity of the problem. Your orthodontist will work up a good financial plan and options depending upon your budget.

The cost of invisalign can vary depending on time of case and how complex it is.
Most importantly, go for a consultation to an Invisalign certified dentist to make sure you are a candidate for this procedure.