document.write( "Question 198153: How long, to the nearest tenth of a year, will it take $3500 to grow to $8000 at 6.5% annual interest compounded semiannually? How long, compounded continuously? \n" ); document.write( "

Algebra.Com's Answer #148655 by stanbon(75887) $\"\"$ $\"About$

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How long, to the nearest tenth of a year, will it take $3500 to grow to $8000 at 6.5% annual interest compounded semiannually?
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\n" ); document.write( "A(t) = P(1+(r/n))^(nt)
\n" ); document.write( "8000 = 3500(1+(0.065/2))^(2t)
\n" ); document.write( "---
\n" ); document.write( "2.2857 = (1+(0.0325)^(2t)
\n" ); document.write( "Take the log to get:
\n" ); document.write( "(2t)log(1.0325) = log(2.2857)
\n" ); document.write( "2t = 25.8472
\n" ); document.write( "t = 12.9236 years
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\n" ); document.write( "How long, compounded continuously?
\n" ); document.write( "A(t) = Pe^(rt)
\n" ); document.write( "8000 = 3500e^(0.065t)
\n" ); document.write( "2.2857 = e^(0.065t)
\n" ); document.write( "Take the natural log to get
\n" ); document.write( "0.065t = ln(2.2857)
\n" ); document.write( "t = 12.718 years
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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