SOLUTION: What nominal rate compounded semi-annually is equivalent to a 10% effective rate?

Algebra ->  Finance -> SOLUTION: What nominal rate compounded semi-annually is equivalent to a 10% effective rate?      Log On


   

Question 1193457: What nominal rate compounded semi-annually is equivalent to a 10%
effective rate?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
What nominal rate compounded semi-annually is equivalent to a 10%
effective rate?
~~~~~~~~~~~~~~~~~~~ 

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


It means that

    %281+%2B+x%2F2%29%5E2 = 1 + 0.1


Simplify and find x


    1+%2B+x%2F2 = sqrt%281.1%29

    x%2F2 = sqrt%281.1%29+-+1

    x = 2%2A%28sqrt%281.1%29-1%29 = 0.097617696.


ANSWER.  x = 9.76%,  rounded.


CHECK.  %281+%2B+0.0976%2F2%29%5E2 = 1.09998144,  which is close enough to  1.1   ( correct !)

Solved.

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

You can find many similar problems solved in my lesson
    - Problems on discretely compound accounts
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,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Logarithms".


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 (!)