$1000 will have doubled when the final amount is $2000

Use the formula:

A = P(1+)nt

where

A = the final amount = $2000
P = the beginning amount = $1000
r = the interest rate per year expressed as a decimal = 0.058
n = the number of times per year the interest is compounded = 12
t = the number of years = the unknown quantity

Substituting the known quantities

2000 = 1000(1+)12t

Divide both sides by 1000

2 = (1+)12t

Take logs of both sides:

log(2) = log(1+)12t

Use the rule of logs:  

log(2) = 12t·log(1+)

Use calculator:

0.3010299957 = 12t·log(1.004833333)

0.3010299957 = 12t(0.0020940335)

0.3010299957 = 0.0251284018t

Divide both sides by 0.0251284018

0.3010299957 = 0.0251284018t

 = t

11.97967138 = t

or approximately 12 years.

Edwin