document.write( "Question 1198670: Mr. Gordon plans to invest $300 at the end of each month in an account that pays 6%, compounded monthly. After how many months will the account be worth $30,000?
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Algebra.Com's Answer #832311 by ikleyn(52790)\"\" \"About 
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\n" ); document.write( "Mr. Gordon plans to invest $300 at the end of each month in an account that pays 6%,
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document.write( "The formula for an Ordinary Annuity saving account compounded monthly  is\r\n" );
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document.write( "    FV = \"P%2A%28%28%281%2Br%2F12%29%5En-1%29%2F%28%28r%2F12%29%29%29\"\r\n" );
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document.write( "where FV is the future value, P is the monthly payment at the end of each month, \r\n" );
document.write( "r is the interest rate per year expressed as a decimal, \r\n" );
document.write( "n is the number of monthly deposits (the number of months).\r\n" );
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document.write( "So, we need to find \" n \" from this equation\r\n" );
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document.write( "    \"%28%281%2B0.06%2F12%29%5En-1%29%2F%28%280.06%2F12%29%29\" = \"FV%2FP\" = \"30000%2F300\" = 100,  \r\n" );
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document.write( "Thus the equation is\r\n" );
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document.write( "    \"%28%281%2B0.005%29%5En-1%29%2F0.005\" = 100.\r\n" );
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document.write( "Rewrite it in this form\r\n" );
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document.write( "    \"1.005%5En-1\" = 0.005*100,\r\n" );
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document.write( "    \"%281.005%29%5En\" = 1 + 0.005*100 = 1.5.\r\n" );
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document.write( "Take the logarithm base 10 of both sides\r\n" );
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document.write( "    n*log(1.005) = log(1.5)\r\n" );
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document.write( "and calculate  \r\n" );
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document.write( "     n = \"log%28%281.5%29%29%2Flog%28%281.005%29%29\" = 81.296  months.\r\n" );
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document.write( "We should round it to the closest greater integer, which is 82 months, \r\n" );
document.write( "in order for the bank be in position to make the last compounding.\r\n" );
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document.write( "ANSWER. 82 months.\r\n" );
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document.write( "CHECK.  \"300%2A%28%281.005%5E82-1%29%2F0.005%29\" = 30316.75, which is greater than 30000;\r\n" );
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document.write( "        \"300%2A%28%281.005%5E81-1%29%2F0.005%29\" = 29867.41, which is less than 30000.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On ordinary annuity saving plan,  see my lessons in this site \r
\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on Ordinary Annuity saving plans \r
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