Question 1193453
.
How long will it take for 74,500 to accumulate to 101,000 if the
interest rate is 10.5 % compounded quarterly?
~~~~~~~~~~~~~~~


<pre>
For the amount of $74,500, compounded quarterly, the future value formula is

    Future Value = {{{74500*(1+0.105/4)^n}}}

where n is the number of quarters.



Therefore, an equation to find "n" is


    101000 = {{{74500*(1+0.105/4)^n}}}


Divide both sides by 74500


    {{{101000/74500}}} = {{{(1+0.105/4)^n}}},

or

    1.355705 = {{{1.02625^n}}}.


Take logarithm base 10 of both sides


    log(1.355705) = n*log(1.02625)


and find "n" using your calculator


    n = {{{log((1.355705))/log((1.02625))}}} = 11.745  quarters.


Finally, round this value 11.745 to the nearest greater integer 12,

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


<U>ANSWER</U>. 12 quarters, or 12/4 = 3 years.
</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 (!)