Question 1206580
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At what rate do you need to invest money into a bank account earning continuously 
compounded interest if you want to double your money in 30 months?
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<pre>
A continuously compouned interest formula is

    A(t) = {{{A(0)*e^(rt)}}},


where A(0) is starting amount (principal deposit); A(t) is the current amount; 
t is the time in years; "r" is the exponential rate coefficient, which is
under the problem's question.


30 months is 2.5 years, so we want

    2A(0) = {{{A(0)*e^(2.5r)}}}.


It implies

    2 = {{{e^(2.5r)}}}.


Take the natural logarithm of both sides

    ln(2) = 2.5*r


and find the rate r

    r = {{{ln(2)/2.5}}} = 0.2773  (rounded).


<U>ANSWER</U>.  The compounded interest rate should be about 0.2773, or 27.73%.
</pre>

Solved.