Suppose that $2500 is invested at an interest rate of 2.5% per year, compounded continuously. After how many years will the initial investment be doubled?

Answer 1

The formula to use can be found and is derived here:
http://www.moneychimp.com/articles/finworks/continuous_compounding.htm

In your case, the answer is obtained by solving
2500*e^0.025Y = 5000
e^.025Y = 2

Y is the number of years and e = 2.71828...

0.025Y = ln2 = 0.69315
Y = 27.7 years