Question 1193457
.
What nominal rate compounded semi-annually is equivalent to a 10%
effective rate?
~~~~~~~~~~~~~~~~~~~


<pre>
Let x be the nominal rate compounded semi-annually, which is equivalent to  10%  effective rate.


It means that

    {{{(1 + x/2)^2}}} = 1 + 0.1


Simplify and find x


    {{{1 + x/2}}} = {{{sqrt(1.1)}}}

    {{{x/2}}} = {{{sqrt(1.1) - 1}}}

    x = {{{2*(sqrt(1.1)-1)}}} = 0.097617696.


<U>ANSWER</U>.  x = 9.76%,  rounded.


<U>CHECK</U>.  {{{(1 + 0.0976/2)^2}}} = 1.09998144,  which is close enough to  1.1   ( correct !)
</pre>

Solved.


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


You can find many similar problems solved in my 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 (!)