document.write( "Question 252472: The amount of money in an account with continuously compounded interest is given by the formula $\"A=Pe%5Ert\"$ , where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 5.5%. Round to the nearest tenth. \n" ); document.write( "

Algebra.Com's Answer #184397 by stanbon(75887) $\"\"$ $\"About$

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Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 5.5%. Round to the nearest tenth.
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\n" ); document.write( "A(t) = Pe^(rt)
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\n" ); document.write( "If you invest \"P\", doubling will give you \"2P\".
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\n" ); document.write( "2P = Pe^(0.055t)
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\n" ); document.write( "2 = e^(0.055t)
\n" ); document.write( "Take the natural log of both sides to solve for \"t\":
\n" ); document.write( "0.055t = ln(2)
\n" ); document.write( "t = 12.6 years
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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