P = $20,000 is the principal

A = 2*P the future value is double the investment amount

t = the time in years

m = 12 compounding periods per year since interest is compounded monthly

n = m*t = 12t compounding periods

r = 0.05 or 5% annual interest

i = r/m = 0.05/12 interest rate per month

A = P(1 + i)^n

Plug the values we have into the formula:

2P = P(1 + 0.05/12)^(12t)

(1 + 0.05/12)^(12t) = 2

12t = log(2)/log(1 + 0.05/12)

........

........

t = 13.89 years

It will take approximately 14 years to double the investment.