document.write( "Question 1161375: 1) Suppose you want to have $500,000 for retirement. Your account earns 9% interest compounded monthly. If you deposit $200 at the end of each month, how long will it take you to reach your goal? Round to the nearest year.\r
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Algebra.Com's Answer #784897 by ikleyn(52781) $\"\"$ $\"About$

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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 = \r\n" );
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document.write( "where FV is the future value, P is the annual payment at the end of each year, n is the number of monthly deposits (of months).\r\n" );
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document.write( "So, we need to find \" n \" from the equation\r\n" );
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document.write( "     =  =  = 2500,  which is the same as\r\n" );
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document.write( "     = 2500.\r\n" );
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document.write( "Rewrite it in this form\r\n" );
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document.write( "     = 0.0075*2500,\r\n" );
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document.write( "     = 1 + 0.0075*2500 = 19.75.\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(1.0075) = log(19.75)\r\n" );
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document.write( "and calculate  \r\n" );
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document.write( "     n =  = 399.2  months = 400 months (rounded to the nearest greater integer value) = 33 years and 4 months.   ANSWER\r\n" );
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document.write( "CHECK.   = 499042.54, which is slightly less than 500000;\r\n" );
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document.write( "         = 502985.38, which is slightly greater than 500000.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On ordinary annuity saving plan, see my lessons in this site \r
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\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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