You have $500 in a savings account. How long will it take to double that amount at an 8% annual interest rate?

Step-by-step explanation:

The formula for compound annual interest is  A = P(1 + r)t  where  

A = Accumulated or final amount  (double $500 = $1000)  

P = Principal or original amount  ($500)  

r = Rate as a decimal (0.08)

t = Time in years  

1000 = 500(1 + 0.08)t

2 = 1.08t  

Take the logarithm of both sides.  I prefer the natural logarithm ln, but if you're more comfortable with base 10 logs they will work just as well  

ln(2) = ln(1.08t)  

ln(2) = t*ln(1.08)

t = ln(2)/ln(1.08)

t = 9.0065 years  

Check:  500*1.089.0065 = $1000