Question 1182865
.
Ramesh earns 5% on a $7,500 investment compounded annually. How long will it take for the investment to reach $50,000?
Compound yearly formula: f(t) = a × (1+b)^t
~~~~~~~~~~~~~~~~~~~~



<pre>
So, what you need is to solve this inequality for time  " t "  in years

    {{{7500*(1+0.05)^t}}} >= 50000.


It is equivalent to the inequality

    {{{1.05^t}}} >= {{{50000/7500}}}

or

    {{{1.05^t}}} >= 6.66667


To solve it, take logarithm base 10 of both sides. You will get

    t*log(1.05) >= log(6.66667),

or

    t >= {{{log((6.66667))/log((1.05))}}} = use your calculator = 38.88 years.


You must round it to the closest greater integer number in order for the bank was in position to make the last compounding.

So your final  <U>ANSWER</U>  is  39 years.
</pre>

Solved.


-------------------


To see many similar solved problems with all detailed explanations &nbsp;(your &nbsp;TEMPLATES), &nbsp;look into these two 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 (!)