Question 1193733
.
What interest rate would be necessary to obtain ​$6500 in 8 years if ​$5000 is the amount of the original investment and the interest is compounded​ yearly?
the interest rate needed is ______ %
​(Do not round until the final answer. Then round to the nearest tenth as​ needed.)
~~~~~~~~~~~~~~~~


<pre>
Use the formula for the future value of an account compounded yearly

    6500 = {{{5000*(1+r)^8}}}


Your task is to determine the unknown rate "r" from this equation.


For it, divide both sides by 5000

    {{{6500/5000}}} = {{{(1+r)^8}}}

    1.3 = {{{(1+r)^8}}}


take logarithm base 10 of both sides

    log(1.3) = 8*log(1+r)


and express

    log(1+r) = {{{log((1.3))/8}}} = 0.014243.


It means that

    1 + r = {{{10^0.014243}}} = 1.03334,


which implies   r = 0.03334 = 3.334%.    <U>ANSWER</U>


<U>CHECK</U>.   {{{5000*1.03334^8}}} = 6500.04  dollars  (which is close enough to the precise future value of $6500).
</pre>

Solved.


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


To see many similar and different solved problems, &nbsp;look into this 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.


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 (!)