If I put 50 dollars a week in a savings account, and I don't touch it, after 13 years with interest of 2.5% how much money will I have saved? Please explain how this works

If I put 50 dollars a week in a savings account, and I don't touch it, after 13 years with interest of 2.5% how much money will I have saved? Please explain how this works
The easiest way to think of it is that every year the bank will credit your account 2.5% of the value of the account at the start of the year. So the first year your investment grows to $50 x 1.025 = $51.25. The second year they add another 2.5%, but this time it's calculated on the $51.25 base that you started the year with. So after two years you have $51.25 x 1.025 = $52.53. And so on. After 13 years you have multiplied your original $50 by 1.025 thirteen times. The math formula is $50 x 1.025^13 = $68.93.

This assumes "simple" compounding once per year. In reality most banks actually add interest compounded more often, either monthly or daily, The math gets more complicated, because you have to figure out the equivalent monthly (or daily) interest rate and then calculate that rate applied over 13 years. If the bank does continuous componding, which is the best deal for you, you actually will end up with $69.20. Here's an explanation of the higher math that's involved:

Compound interest - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Compound_interest)