document.write( "Question 1104177: How long (in years) would $600 have to be invested at 11.2%, compounded continuously, to earn $400 interest? (Round your answer to the nearest whole number.) \n" ); document.write( "

Algebra.Com's Answer #718921 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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How long (in years) would $600 have to be invested at 11.2%, compounded continuously, to earn $400 interest?
\n" ); document.write( " (Round your answer to the nearest whole number.)
\n" ); document.write( ":
\n" ); document.write( "The continuous interest formula: $\"A+=+P%2Ae%5E%28rt%29\"$ , where:
\n" ); document.write( "A = amt after t time
\n" ); document.write( "P = initial amt
\n" ); document.write( "r = interest rate in decimal form
\n" ); document.write( "t = time in years
\n" ); document.write( "When we have $400 interest, the accumulated amt: 600+400 = 1000
\n" ); document.write( " $\"1000+=+600%2Ae%5E%28.112t%29\"$
\n" ); document.write( "we can rewrite it to
\n" ); document.write( " $\"600%2Ae%5E%28.112t%29=1000\"$
\n" ); document.write( " $\"e%5E%28.112t%29=1000%2F600\"$
\n" ); document.write( "reduces to
\n" ); document.write( " $\"e%5E%28.112t%29=5%2F3\"$
\n" ); document.write( "using natural logs, ln of e is 1 therefore
\n" ); document.write( " $\".112t+=+ln%285%2F3%29\"$
\n" ); document.write( ".112t = .5108256
\n" ); document.write( "t = $\".5108256%2F.112\"$
\n" ); document.write( "t = 4.56 ~ 5 years to earn $400 interest \n" ); document.write( "

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