SOLUTION: Mr. Gordon plans to invest $300 at the end of each month in an account that pays 6%, compounded monthly. After how many months will the account be worth $30,000?

The formula for an Ordinary Annuity saving account compounded monthly  is


    FV = 


where FV is the future value, P is the monthly payment at the end of each month, 
r is the interest rate per year expressed as a decimal, 
n is the number of monthly deposits (the number of months).


So, we need to find " n " from this equation


     =  =  = 100,  


Thus the equation is

     = 100.


Rewrite it in this form

     = 0.005*100,

     = 1 + 0.005*100 = 1.5.


Take the logarithm base 10 of both sides

    n*log(1.005) = log(1.5)


and calculate  

     n =  = 81.296  months.


We should round it to the closest greater integer, which is 82 months, 
in order for the bank be in position to make the last compounding.
    

ANSWER. 82 months.


CHECK.   = 30316.75, which is greater than 30000;

         = 29867.41, which is less than 30000.