document.write( "Question 76388: you deposit $2000 in an account that pays 2% annual interest compounded quarterly. How long will it take for the balance to reach $2400?\r
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Algebra.Com's Answer #54798 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "you deposit $2000 in an account that pays 2% annual\r\n" );
document.write( "interest compounded quarterly.  How long will it \r\n" );
document.write( "take for the balance to reach $2400?\r\n" );
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document.write( "I have having trouble completing this problem, \r\n" );
document.write( "please help with the steps.\r\n" );
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document.write( "Tx, H\r\n" );
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document.write( "\"A+=+P%281+%2B+r%2Fn%29%5Ent\"\r\n" );
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document.write( "where\r\n" );
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document.write( "A = final amount\r\n" );
document.write( "P = beginning amount\r\n" );
document.write( "r = annual interest rate expressed as a decimal\r\n" );
document.write( "n = number of times a year interest is compounded\r\n" );
document.write( "t = number of years.\r\n" );
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document.write( "In this problem\r\n" );
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document.write( "A = $2400\r\n" );
document.write( "P = $2000\r\n" );
document.write( "r = .02\r\n" );
document.write( "n = 4 (quarterly)\r\n" );
document.write( "t = unknown\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "\"2400+=+2000%281+%2B+.02%2F4%29%5E%284t%29\"\r\n" );
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document.write( "\"2400+=+2000%281+%2B+.005%29%5E%284t%29\"\r\n" );
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document.write( "\"2400+=+2000%281.005%29%5E%284t%29\"\r\n" );
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document.write( "Divide both sides by 2000\r\n" );
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document.write( "\"2400%2F2000+=+%282000%281.005%29%5E%284t%29%29%2F2000\"\r\n" );
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document.write( "\"1.2+=+1.005%5E%284t%29\"\r\n" );
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document.write( "take the natural log of both sides:\r\n" );
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document.write( "\"ln%281.2%29+=+ln%281.005%5E%284t%29%29\"\r\n" );
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document.write( "Use the rule of logarthims \"ln%28X%5EY%29=Y%2Aln%28X%29\" on the\r\n" );
document.write( "right hand side:\r\n" );
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document.write( "\"ln%281.2%29+=+4tln%281.005%29\"\r\n" );
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document.write( "Divide both sides by \"4ln%281.005%29\"\r\n" );
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document.write( "\"ln%281.2%29%2F%284ln%281.005%29%29+=+%284tln%281.005%29%29%2F%284ln%281.005%29%29+\"\r\n" );
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document.write( "\"ln%281.2%29%2F%284ln%281.005%29%29+=+t\"\r\n" );
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document.write( "Get your calculator and work out the left sides;\r\n" );
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document.write( "\"9.13884909=t\"\r\n" );
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document.write( "At the end of 9 years, the balance will be $2393.36\r\n" );
document.write( "which is short of $2400 by $6.64, then on the next\r\n" );
document.write( "compounding 3 months later, the balance will be \r\n" );
document.write( "$2408.34, which is over $2400 by $8.34.  The balance\r\n" );
document.write( "won't ever reach $2400 exactly, but the first time \r\n" );
document.write( "it will exceed $2400 will be 9 years and 3 months.\r\n" );
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document.write( "Edwin
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