Question 1178200
.


Your starting equation is INCORRECT.


<pre>
The standard translation of the words to Math is THIS equation


    3P = {{{P*(1+r/4)^(4*9)}}},     (1)


where P is the principle amount, r is the nominal annual rate of interest presented as decimal.


4 is the number of quarters in an year and 9 is the number of years.


Canceling P in both sides, you get this equation


    3 = {{{(1+r/4)^36}}}            (2)


with one unknown "r".


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


It gives 


    log(3) = 36*log(1+r/4),

    {{{log((1 + r/4))}}} = {{{log((3))/36}}} = 0.013253

    {{{1 + r/4}}} = 10^0.013253 = 1.030987,  

    {{{r/4}}} = 1.030987 - 1 = 0.030987

    r = 4*0.30987 = 0.123948 = 0.124 (rounded) = 12.4%.      <U>ANSWER</U>



<U>ANSWER</U>.  The nominal annual percentage rate is 12.4%.

         The nominal decimal annual rate is 0.124.



<U>CHECK</U>.  {{{(1+0.124/4)^(4*9)}}} = use your calculator = 3.00.    ! Correct !.
</pre>

Solved.


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<pre>
You can solve equation (2) differently, by taking the root of degree 36 of both sides.


You will get then


    {{{1 + r/4}}} = 3^(1/36) = 1.030987


which leads you to the same final answer for "r".
</pre>


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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 (!)