document.write( "Question 436823: How long does it take $875 to double if it is invested at 8% compounded monthly? \n" ); document.write( "

Algebra.Com's Answer #853283 by ikleyn(53427) $\"\"$ $\"About$

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\n" ); document.write( "How long does it take $875 to double if it is invested at 8% compounded monthly?
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\n" ); document.write( "\n" ); document.write( "        The formulas in the post by @mananth are incorrect; the answer is incorrect \r
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\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
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document.write( "We start from the standard formula for the future value of this compounded account\r\n" );
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document.write( "    FV = ,\r\n" );
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document.write( "where n is the number of monthly compounding.  The value of 'n' is the unknown and is the subject for finding.\r\n" );
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document.write( "We write this equation for the doubled future value\r\n" );
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document.write( "    1750 = .      (1)\r\n" );
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document.write( "We simplify equation (1) step by step\r\n" );
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document.write( "     = .\r\n" );
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document.write( "    2 = .\r\n" );
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document.write( "Take logarithm of both sides \r\n" );
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document.write( "    log(2) = n*log(1+0.08/12).\r\n" );
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document.write( "Express and calculate 'n'\r\n" );
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document.write( "    n =  = 104.318  (approximately).\r\n" );
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document.write( "The number of compounding is an integer number - so, we must round this decimal 104.318\r\n" );
document.write( "to the closest GREATER integer 105 in order for the bank be in position to make the last compounding.\r\n" );
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document.write( "ANSWER.  First time the compounded amount will exceed the doubled principal in 105 months, \r\n" );
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document.write( "         or 8 years and 9 months.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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