P = $500 the principal

r = 0.06 or 6% annual interest rate

m = 12 compounding period per year

i = 0.06/12 = 0.005 interest rate per period

t = the number of years

n = t*12 = 12t total number of compounding periods

A = 2P future value

A = P(1 + i)^n

2P = P(1 + 0.005)^(12t)

(1 + 0.005)^(12t) = 2

12t log(1.005) = log(2)

t = (1/12)(log(2))/(log(1.005))

t = 11.58 years

click here to see the step by step solution of the equation

it will take 11.58 years for the investment to double.