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 #184396 by drk(1908) $\"\"$ $\"About$

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We want our money to double. P = principal, A = 2*principal = 2P. r = 5.5% or 0.055. So, we have
\n" ); document.write( " $\"A+=+Pe%5Ert\"$
\n" ); document.write( " $\"2P+=+Pe%5E0.055%2At\"$
\n" ); document.write( "canceling the P and taking a natural log \"LN\" of both sides, we get
\n" ); document.write( " $\"ln%282%29+=+.055t\"$
\n" ); document.write( "solving for t, we get
\n" ); document.write( "t ~ 12.60 years to the nearest hundredth of a year.
\n" ); document.write( "t ~ 12 years 220 days to the nearest tenth.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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