We know that Nevaeh initially deposited $2,100, and now she has $2,131.50 in her account. The interest earned is $2,131.50 - $2,100 = $31.50. To find out how many months has she been investing her money, we can use the following formula:
Time (in months) = (Interest / Principal) x (12 / Interest Rate)
Where Principal is the initial deposit amount, Interest Rate is the annual interest rate, and Interest is the amount of interest earned.
Plugging in the given values, we get:
Time (in months) = ($31.50 / $2,100) x (12 / 0.06)
Time (in months) = 0.0149 x 200
Time (in months) = 2.98
Since time cannot be in fraction of months, it has to be rounded off. So, Nevaeh has been investing her money for approximately 3 months.