Is it possible to get Breast Augmentation at 16 years of age?

In the United States the Food and Drug Administration mandates that patients be at least 18 years old before undergoing breast augmentation.  From their website:  "The FDA approved saline-filled breast implants for breast augmentation
in women age 18 or older and for breast reconstruction in women of any
age."  Frankly, I do not know what the regulations are in other countries.  You sound like a mature young woman, and an otherwise excellent candidate for breast augmentation.  Unfortunately, you are going to have to wait a couple more years. 

Pursuant to FDA rules, silicone implants should not be used in patients under age 18.  I would encourage you to wait until age 18. It is possible for you to have additional breast development, particularly if you were to go on birth control pills.  Typically, women will gain a bit of weight as they age and that would have an effect on implant size.  It is admirable that you have managed to save enough money to undergo the procedure.  Best wishes.

Aesthetic breast augmentation in the US for patients less than 18yo would require using the implants in an "off label" fashion.  While legal you should understand this.  More importantly is selecting your surgeon.  Make sure you consult with a board certified plastic surgeon (member of the American Society for Aesthetic Plastic Surgery) and make sure you are comfortable that that surgeon has your best interests in mind.  Speaking in generalities, in my opinion there are many reasons to wait to have an aesthetic breast augmentation and few (at best) to have breast augmentation at 16 years old.  If yours is a case of breast reconstruction for a congenital or post-traumatic deformity, then the discussion is entirely different.