document.write( "Question 1206983: how long would it take for 1000 deposited in an account payinv 6% interest compounded countinously to earn 200 interest \n" ); document.write( "

Algebra.Com's Answer #844754 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "how long would it take for 1000 deposited in an account payinv 6% interest
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document.write( "Formula for the future value of a continuously compounded account in this problem is\r\n" );
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document.write( "    FV = ,\r\n" );
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document.write( "where \"t\" is in years, \"e\" is the base of natural logarithms.\r\n" );
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document.write( "So, we write for the total\r\n" );
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document.write( "    1000 + 200 = \r\n" );
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document.write( "or\r\n" );
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document.write( "    1200 = .\r\n" );
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document.write( "Now we solve this equation, step by step, and find time \"t\".\r\n" );
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document.write( "     = \r\n" );
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document.write( "    1.2 =  = \r\n" );
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document.write( "Next, take the natural logarithm of both sides\r\n" );
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document.write( "    ln(1.2) = 0.06*t\r\n" );
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document.write( "    t =  = 3.038692613\r\n" );
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document.write( "So, the  ANSWER  is that the time to earn 200 interest is about 3 years.\r\n" );
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document.write( "                 (More precisely, 3 years and 15 days).\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) solved problems on continuously compounded accounts, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Problems on continuously compound accounts \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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