Question 1178392
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Jimmy invests ​$19,000 in an account that pays 6.05​% compounded quarterly. 
How long​ (in years and​ months) will it take for his investment to reach ​$25,000​?
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<pre>
For the amount of $19000, compounded quarterly, the future value formula is

    Future Value = {{{19000*(1+0.0605/4)^n}}}

where n is the number of quarters.



Therefore, our equation to find "n" is


    25000 = {{{19000*(1+0.0605/4)^n}}}


Divide both sides by 19000


    {{{25000/19000}}} = {{{(1+0.0605/4)^n}}},

or

    1.315789 = {{{1.015125^n}}}.


Take logarithm base 10 of both sides


    log(1.315789) = n*log(1.015125)


and find "n" using your calculator


    n = {{{log((1.315789))/log((1.015125))}}} = 18.28  quarters.


Finally, round this value 18.28 to the nearest greater integer 19,

in order for the bank was in position to make the last compounding.


<U>ANSWER</U>. 19 quarters, or 19*3 = 57 months, or 4 years and 9 months.
</pre>

Solved.


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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 (!)