Adding 5% interest to an account yearly has the same effect as taking 105% of its current value every year (you're taking all of your money - 100% of it - and adding an extra 5%, getting you 100% + 5% = 105%). This means that, if we started with $1000, after the first year, we'd have
1000(1.05) = $1050
after the second, and third years
1000(1.05)(1.05) = 1000(1.05)² = $1102.50
1000(1.05)(1.05)(1.05) = 1000(1.05)³ ≈ $1157.62
We can see a pattern starting to emerge. The 1000 always stays the same since its our starting value, but the power of the 1.05 goes up by 1 every year. In general, if we call the current value of the account in dollars y and the number of years it's been in the account x, then we can write this pattern generally as
