Equation: S = 70x + 1000
S = The total amount of money you will have in the bank.
x = The total # of months that you deposited $70.
In a real world situation though, you have to consider how much money the bank gives you every month just for saving your money with them. It is in the form of a percentage called a rate. In Washington, the rate for a personal savings account (for youth accounts too) is 0.01% at Bank of America. Read on, you'll get it!
You start with 1000 and deposit 70 so that you have 1070 by the end of your first month right? Take the 1070 and multiply it by 0.01. It comes out to 10.70 right? That $10.70 is the amount the bank gives you by the end of your first month! So now you have 1070 + 10.70. That's $1080.70 right?
Every month the bank gives you 0.01% of the amount you have in the bank so far. So for the next month, start with 1080.70 and do the same thing. Multiply 1080.70 by 0.01 to find how much the bank gives you. Then add that amount to 1080.70. It comes out to 1091.5 by the way.
Which means the above equation will not give you the right number of months it will take you to save a certain amount of money in a real life situation because it doesn't include the 0.01% that the bank gives you.
Anyways, the answer to your second question using the equation:
S = 70x + 1000
10,000 = 70x +1000
Subtract 1000 from both sides
9000 = 70x
Divide both sides by 70
x = 128.57 months
128.57 months is 10.71 years.
But in the real world it will take you much less time to save up $10,000 because of the money the bank gives you just for saving with them which I talked about before. Accountants figure out these types of calculations. They can use Excel to do it. I just did. In the real world, it will take you 76 months to save $10,020.67. 76 months is 6.3 years. 6.3 years is 6 years and 4 months. Big difference from 10.71 years!!
But 6 years and 4 months is still a long time. In 1 year you will have saved up $2003.44 if you deposit $70 every month. In 2yrs it will be $3145.31. Finding out that you can make more money in less time is very interesting especially if you know how and why. Which is probably one of the top reasons to learn math. Hope that helped!