Question 436823
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How long does it take $875 to double if it is invested at 8% compounded monthly?
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        The formulas in the post by @mananth are incorrect;  the answer is incorrect 

        and is given in the incorrect form.


        I came to bring a correct solution.



<pre>
We start from the standard formula for the future value of this compounded account

    FV = {{{875*(1+0.08/12)^n}}},

where n is the number of monthly compounding.  The value of 'n' is the unknown and is the subject for finding.


We write this equation for the doubled future value

    1750 = {{{875*(1+0.08/12)^n}}}.      (1)


We simplify equation (1) step by step

    {{{1750/875}}} = {{{(1+0.08/12)^n}}}.

    2 = {{{(1+0.08/12)^n}}}.


Take logarithm of both sides 

    log(2) = n*log(1+0.08/12).


Express and calculate 'n'

    n = {{{log((2))/log((1+0.08/12))}}} = 104.318  (approximately).


The number of compounding is an integer number - so, we must round this decimal 104.318
to the closest GREATER integer 105 in order for the bank be in position to make the last compounding.


<U>ANSWER</U>.  First time the compounded amount will exceed the doubled principal in 105 months, 

         or 8 years and 9 months.
</pre>

Solved correctly.