Question 1178219
.
<pre>

The standard translation of the words to Math is THIS equation


    2P = {{{P*(1+0.09/4)^(4*t)}}},     (1)


where P is the principal amount, t is the time in years.


Canceling P in both sides, you get this equation


    2 = {{{(1+0.09/4)^(4t)}}}            (2)


with one unknown "t".


The standard method to solve it is to take logarithm of both sides.


It gives 


    log(2) = 4t*log(1+0.09/4),

    
    t = {{{log((2))/(4*log((1+0.09/4)))}}} = 7.78.      


Now you need to round this number to the nearest greater integer in order for the bank
was in position to make the last compounding.



<U>ANSWER</U>.  8 years is required.
</pre>

Solved.


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To see many other similar (and different) solved problems, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/percentage/lessons/Compound-interest-percentage-problem.lesson>Compound interest percentage problems</A> 

&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, &nbsp;and learn the subject from there.



After reading these lessons, &nbsp;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 lessons are 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 (!)