SOLUTION: 1) Suppose you want to have $500,000 for retirement. Your account earns 9% interest compounded monthly. If you deposit $200 at the end of each month, how long will it take you to r

The formula for an Ordinary Annuity saving account compounded monthly  is


    FV = 


where FV is the future value, P is the annual payment at the end of each year, n is the number of monthly deposits (of months).


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


     =  =  = 2500,  which is the same as

     = 2500.


Rewrite it in this form

     = 0.0075*2500,

     = 1 + 0.0075*2500 = 19.75.


Take the logarithm base 10 of both sides

    n*log(1.0075) = log(19.75)


and calculate  

     n =  = 399.2  months = 400 months (rounded to the nearest greater integer value) = 33 years and 4 months.   ANSWER
    

CHECK.   = 499042.54, which is slightly less than 500000;

         = 502985.38, which is slightly greater than 500000.