document.write( "Question 1153381: How long does it take for an investment to double in value if it is invested at 4% compounded quarterly question mark Compounded continuously? \n" ); document.write( "

Algebra.Com's Answer #775804 by math_helper(2461) $\"\"$ $\"About$

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document.write( "     (1)
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document.write( "where
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document.write( "F = future value
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document.write( "P = present value
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document.write( "r = annual interest rate
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document.write( "n = number of payments per year
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document.write( "t = number of years\r
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document.write( "This problem asks to find t for F=2P,  r=4% (0.04), and n=4 interest payments per year:
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document.write( "Cancel P from both sides, and simplify where possible:
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document.write( "Take ln() of both sides:
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document.write( "Solve for t:
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document.write( " years\r
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document.write( " years  (about 17yrs, 151.6days}\r
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document.write( "--------------
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document.write( "For continuous compounding:
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document.write( "   (2)\r
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document.write( "[ ----------------------\r
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document.write( "An aside: formula (2) can be derived by taking the limit of (1) as n goes to infinity:
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document.write( "     
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document.write( "   Replace r/n by 1/(n/r) and raise the inner expression first to the 'n/r'
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document.write( "     power, and then to the 'rt' power (so the r's would cancel if we carried
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document.write( "     it out):
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document.write( "  
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document.write( "   The green expression has a limit of 'e' as n-->infinity:
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document.write( "  
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document.write( " years (about 17yrs, 120days)\r
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