Question 33003
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A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and 
continuous compounding, what is the answer?
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        The solution in the post by the other tutor is fatally incorrect.

        I came to bring a correct solution.



<pre>
The formula for the future value at continuous compounding is 

    FV = {{{A*e^(r*t)}}},    (1).


where A is the deposited amount, 'r' is the nominal interest rate and 't' is the time in years,
'e' is the base of natural logarithms (e = 2.71828...)


In your problem, A = 10,000 dollars,  FV= 20,000 dollars,  r = 0.1.


So, formula (1) takes the form

    20000 = {{{10000*e^(0.1*t)}}}.


It implies

    {{{20000/10000}}} = {{{e^(0.1*t)}}},

    2 = {{{e^(0.1*t)}}}.


Take natural logarithm of both sides 

    ln(2) = 0.1*t

    t = {{{ln(2)/0.1}}} = 6.93147 years.


<U>ANSWEWR</U>.  The time to double the deposited amount is about  6.93 years under given conditions.
</pre>

Solved correctly with complete explanations.