document.write( "Question 1164309: A sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long will it take the investment to grow to $ 400,000? \n" ); document.write( "

Algebra.Com's Answer #788629 by ikleyn(52832) $\"\"$ $\"About$

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document.write( "The formula for this account is\r\n" );
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document.write( "    FV = ,\r\n" );
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document.write( "where FV is the future value and \"n\" is the number of quarters.\r\n" );
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document.write( "So, you should solve this equation to find n\r\n" );
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document.write( "    400000 = .\r\n" );
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document.write( "First, divide both sides by 250000.  You get\r\n" );
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document.write( "     = ,   or\r\n" );
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document.write( "    1.6 = .\r\n" );
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document.write( "Next, take logarithm base 10 of both sides\r\n" );
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document.write( "    log(1.6) = n*log(1.03).\r\n" );
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document.write( "Hence,  n =  = 15.90 (rounded).\r\n" );
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document.write( "You want to find the number of quarters, which is an integer number.\r\n" );
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document.write( "Therefore, you round the value of 15.90 to the nearest greater integer, where next compounding will happen.\r\n" );
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document.write( "In this way, you get your\r\n" );
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document.write( "ANSWER.  16 quarters,  or 4 years.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar 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
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\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
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\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
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Logarithms\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\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
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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