Question 1206983
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how long would it take for 1000 deposited in an account payinv 6% interest 
compounded countinously to earn 200 interest
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<pre>
Formula for the future value of a continuously compounded account in this problem is

    FV = {{{1000*e^(0.06*t)}}},


where "t" is in years, "e" is the base of natural logarithms.


So, we write for the total

    1000 + 200 = {{{1000*e^(0.06*t)}}}

or

    1200 = {{{1000*e^(0.06*t)}}}.


Now we solve this equation, step by step, and find time "t".

    {{{1200/1000}}} = {{{e^(0.06*t)}}}

    1.2 =  = {{{e^(0.06*t)}}}


Next, take the natural logarithm of both sides

    ln(1.2) = 0.06*t

    t = {{{ln(1.2)/0.06}}} = 3.038692613


So, the  <U>ANSWER</U>  is that the time to earn 200 interest is about 3 years.

                 (More precisely, 3 years and 15 days).
</pre>

Solved.


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To see many other similar &nbsp;(and different) &nbsp;solved problems on continuously compounded accounts, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Problems-on-continuously-compound-accounts.lesson>Problems on continuously compound accounts</A> 

in this site.


After reading this lesson, &nbsp;you will tackle such problems on your own without asking for help from outside.