Okay, I am only suggesting this because I see what my sis-in-law has turned into...she's 17 now and depends on mommy and daddy FOR EVERYTHING!!! She finally got a job last year and STILL hasn't learned a thing! Only that she can do what she wants, throw away her money and mom and dad will pay for gas and phone bills. Not to judge, I love her...but she shows no respect when it comes to her parents. I have never ONCE in the 13 years that I've known her seen her put a dish in the dishwasher, sweep a floor, vacuume, pick up her room etc. She's not to blame because my mother and father-in-law are the one's who did this to her. She's 9 years younger than her brother and sister so she was treated WAY differently. My hubby and other sis-in-law had to help around the house...NO PAY...and they got jobs when they were 14 or 15 and were made to save part of their paycheck. They also had to keep up with the house or jobs would be lost. They both have a huge sense of reaponsibility now in their adult life and have their parents to thank for it.
So...that being said...
Have you discussed her getting a part time job? She's old enough to work now, and it is summer so school won't get in the way. While school is in she's not allowed to work past a certain time anyway. This will teach her even more responsibility and she'll probably be less willing to lay the guilt trip on a boss. Also, her boss won't be a soft on her. You know how it's hard to say no to your kids sometimes. I get it...I'm a mom too. Obviously there will be times when you will probably need to spot her an exta $20 or $30 and that's fine.
If I were to let her have a job I would make it clear that she would STILL have to do things around the house. If not...she has to leave her job. Trust me...she'll use work as an excuse not to do stuff at home. That's how my mom handled my first job experience...I was 12 turning 13 at the time...way back when Meijer still had kids bagging groceries. I was able to work but I also had school and housework to juggle. I loved having my own money!
I know this isn't what you asked for...just wanted to give you a different suggestion.
Good luck in whatever you do, and I commend you for making her save that $3! Not enough people teach their kids to save...
P.S. My girls are 4 and 6 and they put away laundry, make their beds, keep their toys cleaned up, put their shoes away, hand up their coats, clear the table, set the table, load/unload the dishwasher, sometimes they'll help fold laundry (as best as they can). As soon as they are tall enough and old enough, they'll be graduating to toilets and floors!