Question

suppose that you put $2,500 into retirement account that grows with an interest rate of 5.25 % compounded once each year after how many years will the balance of the account be at least $15,000?

Answer 1

You will need to use this formula:
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = [log(15,000) - log(2,500)] / log (1.0525)

4.1760912591 - 3.3979400087 / 0.0222221045 =
0.7781512504 / 0.0222221045 =

35.0169917705 years
About 35 years

You'll find the formula here: http://www.1728.org/compint2.htm
And a compound interest calculator here: http://www.1728.org/compint.htm
(You'll find both are helpful for this problem).