document.write( "Question 823169: How long will it take for 1000 to double, in an investment, when interest is compounded monthly at the rate of 5.8% per year? \n" ); document.write( "

Algebra.Com's Answer #495306 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "$1000 will have doubled when the final amount is $2000\r\n" );
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document.write( "Use the formula:\r\n" );
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document.write( "A = P(1+)^nt\r\n" );
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document.write( "where\r\n" );
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document.write( "A = the final amount = $2000\r\n" );
document.write( "P = the beginning amount = $1000\r\n" );
document.write( "r = the interest rate per year expressed as a decimal = 0.058\r\n" );
document.write( "n = the number of times per year the interest is compounded = 12\r\n" );
document.write( "t = the number of years = the unknown quantity\r\n" );
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document.write( "Substituting the known quantities\r\n" );
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document.write( "2000 = 1000(1+)^12t\r\n" );
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document.write( "Divide both sides by 1000\r\n" );
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document.write( "2 = (1+)^12t\r\n" );
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document.write( "Take logs of both sides:\r\n" );
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document.write( "log(2) = log(1+)^12t\r\n" );
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document.write( "Use the rule of logs:  \r\n" );
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document.write( "log(2) = 12t·log(1+)\r\n" );
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document.write( "Use calculator:\r\n" );
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document.write( "0.3010299957 = 12t·log(1.004833333)\r\n" );
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document.write( "0.3010299957 = 12t(0.0020940335)\r\n" );
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document.write( "0.3010299957 = 0.0251284018t\r\n" );
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document.write( "Divide both sides by 0.0251284018\r\n" );
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document.write( "0.3010299957 = 0.0251284018t\r\n" );
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document.write( " = t\r\n" );
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document.write( "11.97967138 = t\r\n" );
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document.write( "or approximately 12 years.\r\n" );
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document.write( "Edwin

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