document.write( "Question 1207352: if money can earn 4.0% compounded monthly, how long will it take you to accumulate $ 1 million in your RRSP if you contribute $1440 at the end of each month? \n" ); document.write( "

Algebra.Com's Answer #845174 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "If money can earn 4.0% compounded monthly, how long will it take you to accumulate
\n" ); document.write( "$1,000,000 in your RRSP if you contribute $1440 at the end of each month?
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document.write( "Use the formula for an Ordinary Annuity saving account compounded monthly \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 payment at the end of each month, \r\n" );
document.write( "r is the interest rate per year expressed as decimal, \r\n" );
document.write( "n is the number of monthly deposits (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( "     =  =  = 694.4444444\r\n" );
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document.write( "     = . \r\n" );
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document.write( "Rewrite it in this form\r\n" );
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document.write( "     = 2.314815,\r\n" );
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document.write( "     = 1 + 2.314815 = 3.314815.\r\n" );
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document.write( "Take logarithm base 10 of both sides\r\n" );
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document.write( "    n*log(1+0.04/12) = log(3.314815)\r\n" );
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document.write( "and calculate  \r\n" );
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document.write( "     n =  = 360.1194131 months.\r\n" );
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document.write( "Round it to the closest greater month, which is 361 months, \r\n" );
document.write( "in order for the bank would be in position to compete the last compounding.\r\n" );
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document.write( "361 months is the same as 30 years and 1 month.\r\n" );
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document.write( "ANSWER.  361 months, or 30 years and 1 month.\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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