document.write( "Question 1195860: If money is worth 12% per annum, compounded monthly, how long will it take the principal P to become four times the original value? \n" ); document.write( "
Algebra.Com's Answer #828445 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "If money is worth 12% per annum, compounded monthly,
\n" ); document.write( "how long will it take the principal P to become four times the original value?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            The problem's formulation is  INCORRECT,  since the terms are used incorrectly.\r
\n" ); document.write( "\n" ); document.write( "            The correct formulation is as follows:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "                If an account  \"highlight%28highlight%28earns%29%29\"  12% per annum, compounded monthly, \r\n" );
document.write( "                how long will it take the principal P to become four times the original value?\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            In this formulation,  the solution is below.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Write equation, as you read the problem, for the account, which grows as described\r\n" );
document.write( "\r\n" );
document.write( "    4P = \"P%2A%281%2B0.12%2F12%29%5En\",\r\n" );
document.write( "\r\n" );
document.write( "where P is the principal and n is the number of months (= the number of compounding periods)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Cancel P in both sides to get\r\n" );
document.write( "\r\n" );
document.write( "    4 = \"%281+%2B+0.01%29%5En\",\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "    4 = \"1.01%5En\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Take logarithm base 10 of both sides\r\n" );
document.write( "\r\n" );
document.write( "    log(4) = n*log(1.01),\r\n" );
document.write( "\r\n" );
document.write( "      n    = \"log%28%284%29%29%2Flog%28%281.01%29%29\" = 139.32 months.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Round the months to the closest larger integer in order for the bank\r\n" );
document.write( "would be in position to make the last compounding.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  140 months, or  11 years and 8 months.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The term  \" the money is worth \"  is used when the money is borrowed.\r
\n" ); document.write( "\n" ); document.write( "In this problem,  the money is  \"highlight%28highlight%28invested%29%29\",  so the relevant term is  \" the money  EARNS \".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "=================\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To see many other similar  (and different)  solved problems,  look into the 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" );