document.write( "Question 183182: You deposit $800 in an account that pays 9% annual intrest compounded monthly. About how many years will it take for the account balance to reach $2400? Convert this to years and months. \n" ); document.write( "
Algebra.Com's Answer #137590 by Edwin McCravy(20056)\"\" \"About 
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You deposit $800 in an account that pays 9% annual
\n" ); document.write( "interest compounded monthly. About how many years
\n" ); document.write( "will it take for the account balance to reach $2400?
\n" ); document.write( "Convert this to years and months.
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document.write( "\"A+=+P%281%2BR%2FN%29%5E%28NT%29\"\r\n" );
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document.write( "where A = Final Amount = $2400\r\n" );
document.write( "      P = Beginning Amount = $800\r\n" );
document.write( "      R = Rate expessed as a decimal = .09\r\n" );
document.write( "      N = Number of compoundings per year = 12\r\n" );
document.write( "      T = Number of years = ?  (What we must find)\r\n" );
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document.write( "We substitute for all but T\r\n" );
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document.write( "\"A+=+P%281%2BR%2FN%29%5E%28NT%29\"\r\n" );
document.write( "\"2400+=+800%281%2B.09%2F12%29%5E%2812T%29\"\r\n" );
document.write( "\"2400+=+800%281.0075%29%5E%2812T%29\"\r\n" );
document.write( "\"2400%2F800+=+%28800%281.0075%29%5E%2812T%29%29%2F800\"\r\n" );
document.write( "\"3+=+%281.0075%29%5E%2812T%29\"\r\n" );
document.write( "\"ln%283%29=ln%281.0075%29%5E%2812T%29\"\r\n" );
document.write( "\"ln%283%29=12T%2Aln%281.0075%29\"\r\n" );
document.write( "\"ln%283%29%2F%2812ln%281.0075%29%29=T\"\r\n" );
document.write( "\"ln%283%29%2F%2812ln%281.0075%29%29=T\" \r\n" );
document.write( "\"1.098612289%2F%2812%2A.0074720148%29=T\"\r\n" );
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document.write( "\"12.25252171=T\"\r\n" );
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document.write( "12 years\r\n" );
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document.write( "To get the months, multiply the decimal \r\n" );
document.write( "part \".25252171\" by 12\r\n" );
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document.write( "\"3.030260563\" months\r\n" );
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document.write( "or about 12 years, 3 months.\r\n" );
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document.write( "Edwin
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