document.write( "Question 1198969: You are investing money at 9.5 percent annual interest, compounded continuously. It will take you {insert here} years to double your investment. \n" ); document.write( "

Algebra.Com's Answer #832996 by Shin123(626) $\"\"$ $\"About$

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The formula for continuous compounding is $\"P%2Ae%5E%28rt%29\"$ , where $\"P\"$ is the principal, $\"e\"$ is Euler's number, $\"r\"$ is the interest rate, and $\"t\"$ is the number of years.
\n" ); document.write( "We are trying to find $\"t\"$ in the equation $\"2P=P%2Ae%5E%28rt%29\"$ . Since we know that the interest rate is $\"0.095\"$ , we can put that into the equation to get $\"2P=P%2Ae%5E%280.095%2At%29\"$ . Dividing both sides by $\"P\"$ , we get $\"e%5E%280.095%2At%29=2\"$ . Taking the natural log of both sides, we get $\"0.095%2At=ln%282%29\"$ . Finally, dividing both sides by $\"0.095\"$ gives us $\"t=ln%282%29%2F0.095\"$ . Plugging into a calculator, we get that $\"t\"$ is approximately $\"highlight%287.296%29\"$ years. \n" ); document.write( "

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