Question 1195860
.
If money is worth 12% per annum, compounded monthly, 
how long will it take the principal P to become four times the original value?
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            The problem's formulation is  INCORRECT,  since the terms are used incorrectly.

            The correct formulation is as follows:


<pre>
                If an account  {{{highlight(highlight(earns))}}}  12% per annum, compounded monthly, 
                how long will it take the principal P to become four times the original value?
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In this formulation, &nbsp;the solution is below.



<pre>
Write equation, as you read the problem, for the account, which grows as described

    4P = {{{P*(1+0.12/12)^n}}},

where P is the principal and n is the number of months (= the number of compounding periods)


Cancel P in both sides to get

    4 = {{{(1 + 0.01)^n}}},

or

    4 = {{{1.01^n}}}.


Take logarithm base 10 of both sides

    log(4) = n*log(1.01),

      n    = {{{log((4))/log((1.01))}}} = 139.32 months.


Round the months to the closest larger integer in order for the bank
would be in position to make the last compounding.


<U>ANSWER</U>.  140 months, or  11 years and 8 months.
</pre>

Solved.



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The term &nbsp;" the money is worth " &nbsp;is used when the money is borrowed.

In this problem, &nbsp;the money is &nbsp;{{{highlight(highlight(invested))}}}, &nbsp;so the relevant term is &nbsp;" the money &nbsp;EARNS ".



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

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

in this site, and learn the subject from there.



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


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic "<U>Logarithms</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.



Happy learning (!)