Question 1183163
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Suppose you have $8000 deposited in an account with interest compounded semiannually. 
After 8 years, the account has grown to $9300. What is the interest rate on this account? 
(Round your answer to the nearest hundredth of a percent)
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<pre>
Your starting equation is

    9300 = {{{8000*(1+r/2)^(2*8)}}}


and your goal is to find the unknown annual interest rate r (as decimal).


You simplify your equation

    {{{9300/8000}}} = {{{(1+r/2)^16}}},

    1.1625 = {{{(1+r/2)^16}}}.


You take logarithm base 10 from both sides

    log(1.1625) = 16*log(1+r/2)

and find

    {{{log((1+r/2))}}} = {{{log((1.1625))/16}}} = 0.004087.


Next, you take exponent of both sides and get

    {{{1 + r/2}}} = {{{10^0.004087}}} = 1.009455.


Hence,

    r/2 = 1.009455 - 1 = 0.009455;   r = 2*0.009455 = 0.01891.


Thus the annual percentage compound rate is 1.89%.    <U>ANSWER</U>
</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 (!)