document.write( "Question 1193457: What nominal rate compounded semi-annually is equivalent to a 10%
\n" ); document.write( "effective rate? \n" ); document.write( "
Algebra.Com's Answer #825483 by ikleyn(52786)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "What nominal rate compounded semi-annually is equivalent to a 10%
\n" ); document.write( "effective rate?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Let x be the nominal rate compounded semi-annually, which is equivalent to  10%  effective rate.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that\r\n" );
document.write( "\r\n" );
document.write( "    \"%281+%2B+x%2F2%29%5E2\" = 1 + 0.1\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and find x\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"1+%2B+x%2F2\" = \"sqrt%281.1%29\"\r\n" );
document.write( "\r\n" );
document.write( "    \"x%2F2\" = \"sqrt%281.1%29+-+1\"\r\n" );
document.write( "\r\n" );
document.write( "    x = \"2%2A%28sqrt%281.1%29-1%29\" = 0.097617696.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  x = 9.76%,  rounded.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  \"%281+%2B+0.0976%2F2%29%5E2\" = 1.09998144,  which is close enough to  1.1   ( correct !)\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You can find many similar problems solved in my lesson\r
\n" ); document.write( "\n" ); document.write( "    - Problems on discretely compound accounts \r
\n" ); document.write( "\n" ); document.write( "in this site, and learn the subject from there.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "After reading this lesson, you will tackle such problems on your own without asking for help from outside.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Logarithms\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );