document.write( "Question 1182420: How long will it take $3,000 to grow to $14,000 if it is invested at 5% compounded monthly?\r
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Algebra.Com's Answer #853600 by n2(47) $\"\"$ $\"About$

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\n" ); document.write( "How long will it take $3,000 to grow to $14,000 if it is invested at 5% compounded monthly?
\n" ); document.write( "How many years?
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\n" ); document.write( "\n" ); document.write( "        In the post by @CPhill, the answer is incorrect.\r
\n" ); document.write( "\n" ); document.write( "        In this problem, same as many other similar problems,\r
\n" ); document.write( "\n" ); document.write( "        the answer should be expressed in integer number of compounding periods.\r
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document.write( "Principal P = 3000\r\n" );
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document.write( "Amount= 14000\r\n" );
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document.write( "number of compounding = n\r\n" );
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document.write( "compounded 12 times per year\r\n" );
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document.write( "Nominal rate per year = 5%\r\n" );
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document.write( "Effective rate per month  r = 0.05/12\r\n" );
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document.write( "Future value = \r\n" );
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document.write( "14000 = \r\n" );
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document.write( "4.666666667 = \r\n" );
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document.write( "log(4.666666667) = \r\n" );
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document.write( "n =  = 370.4764986  (approx.)\r\n" );
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document.write( "This decimal number,  370.4764986,  should be rounded up to the closest integer number 371\r\n" );
document.write( "in order for the bank would be in position to make the last compounding.\r\n" );
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document.write( "ANSWER.  The value at the account first time will exceed $14000 after 371 month, or 30 years and 11 months.\r\n" );
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\n" ); document.write( "\n" ); document.write( "When solving such problems on discrete compounding, always remember that the future value
\n" ); document.write( "is NOT a continuous function of time. In opposite, it is piecewise constant function,
\n" ); document.write( "which changes its values at the end of each compounding period, ONLY.\r
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