Question

Sarah deposits $600 in a savings account that pays 2.5% per year. What is the minimum number of years it would take for the amount in her account to be more than $800, provided no more money is deposited in the account?

Answer 1

Here is the compound interest formula solved for years:
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = {log(800) - log(600)} ÷ log(1.025)
Years = {2.903089987 -2.7781512504} / 0.010723865392
Years = { 0.1249387366 } / 0.010723865392
Years = 11.6505319708
That's how many years it takes for the $600 to become exactly $800.00
The question specifically asks how long for the money to be MORE than $800.00?

So, if we enter 800.01 into the equation, then the answer is
Years = {log(800.01) - log(600)} ÷ log(1.025)
Years = {2.9030954156 -2.7781512504} / 0.010723865392
Years = 0.1249441652 / 0.010723865392
Years = 11.6510381875