SOLUTION: Suppose you put $ 525 a month for retirement into an annuity earning 7% compounded monthly. If you need $ 350000 to retire, in how many years will you be able to retire? Years =

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 month, 
r is the interest rate per year expressed as decimal, 
n is the number of monthly deposits (of months).


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


     =  =  = 666.667,  

which is the same as

     = 666.667.


Rewrite it in this form

     = 0.005833*666.667,

     = 1 + 0.005833*666.667 = 4.88867.


Take the logarithm base 10 of both sides

    n*log(1.005833) = log(4.88867)


and calculate  

     n =  = 272.75  months = 273 months (rounded to the nearest greater integer value) = 22 years and 9 months.   ANSWER
    

CHECK.   = 350400, which is slightly greater than 350000;

         = 347846, which is slightly lesser than 350000.


ANSWER.  273 months is needed,  or 22.75 years = 22 years and 9 months.

         If to round to closest year, then  23 years is just enough;  22 years is not enough yet.