document.write( "Question 63272: How long will it take $500.00 to grow to $2,000.00 at an interest rate of 4% if the interest is compounded continuously. \n" ); document.write( "

Algebra.Com's Answer #44043 by Edwin McCravy(20060) $\"\"$ $\"About$

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How long will it take $500.00 to grow to $2,000.00 at an interest rate of 4% if\r\n" );
document.write( "the interest is compounded continuously.\r\n" );
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document.write( "All exponential growth or decay problems come from this formula:\r\n" );
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document.write( "A = Pe^rt\r\n" );
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document.write( "Where P is the original amount, and A is the final amount, and r is the\r\n" );
document.write( "yearly rate for continuous compounding problems.\r\n" );
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document.write( "So we substitute A = 2000, P = 500, and r - .04 and solve for t:\r\n" );
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document.write( "2000 = 500e^.04t\r\n" );
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document.write( "Divide both sides by 500\r\n" );
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document.write( "4 = e^.04t\r\n" );
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document.write( "Rewrite that using the rule:\r\n" );
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document.write( "The exponential equation Y = e^X can be rewritten as the \r\n" );
document.write( "logarithmic equation X = ln(Y).\r\n" );
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document.write( ".04t = ln(4)\r\n" );
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document.write( "Divide both sides by .04\r\n" );
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document.write( "  t = ln(4)/.04 = 1.386294361/.04 = 34.65735903\r\n" );
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document.write( "or more than 34 1/2 years.  By the way, things that\r\n" );
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document.write( "cost $500 34 years ago cost a lot MORE THAN $2000 today.\r\n" );
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document.write( "In 1972, I paid $30,000 for a house that is worth $250,000\r\n" );
document.write( "today!!!!!!\r\n" );
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document.write( "Moral of the story: Investing at 4% interest does not\r\n" );
document.write( "come close to keeping up with inflation.\r\n" );
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document.write( "Edwin

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