In addition, when should I open a savings account at our bank for my kids; and give them accountability over it?
We started with our son about age 5 or so. He was at the time old enough to understand that you buy stuff using money.
We don't give allowance, rather we made up a job chart that he can put checks on, and give him a small amount for each job that he does. This is meant to enforce the idea of 'work and get paid, don't work don't get paid', and associate the concept of work and money.
We also try to teach him the concept of giving, spending and saving, by having envelopes with those words on them and dividing the 'commission' money between them. The give money is used for a charitable organization. The save money is used in a couple of ways - either to save for a large item that he wants, or to put into a savings account. The spend it money he is free to buy whatever he wants with.
We got this plan from the Dave Ramsey Show, and it has been really good so far. The best thing about it is that when we are at the store and he sees something he wants, we can ask 'did you bring your money?' This keeps the begging down to a minimum and also helps us teach him to make a list of stuff he wants and can save for.
My daughter is two, and she has a piggy bank that regularly dines on my pocket change. When that bank is worth $100 or so I will make it a regular high yield savings account. Then I will either setup a regular $10/month transfer into it, or something depending on what we can afford.
My plan is then to offer my kid an allowance when she can understand the concept of money. My clever idea is I will offer her a savings plan with the Bank of Daddy. If she lets me keep her allowance for the week, I will give her double the amount plus a percentage the next week. If she does it she will soon see the magic of saving money and how banks pay your for the privilege.
I don't know when I will give her access to the savings account with actual cash. I will show it to her, and review it with her so she can track her money, but I need to know that she has some restraint before I open the gates to her.
It's never too early, but age 3 is when we started a piggy bank. Age 4 is when we opened a bank account. When you go shopping with your children, discuss what items cost (such as bread, milk, books, etc.) Start teaching them that everything has a value...then relate it to how much they have saved.
Kids need to learn 3 basic things from their parents: how to save/invest, how to spend wisely, how to share/donate