document.write( "Question 747829: Find the time required for money invested at an annual rate of 6% to double in value if the investment is compounded monthly. Round to the nearest hundredth of a year. (Hint: you will need to choose a starting value.) \n" ); document.write( "
Algebra.Com's Answer #455177 by FrankM(1040)\"\" \"About 
You can put this solution on YOUR website!
No starting value is required. You are simply asking how many time periods are required to double a value. Here, 6% is .5% per month.
\n" ); document.write( "Before solving, note there is a \"rule of 72.\" A close guess is that 72/6 is the years it takes to double. 12 years will be close to the answer. \r
\n" ); document.write( "\n" ); document.write( "2=(1.005^N) \r
\n" ); document.write( "\n" ); document.write( "ln2=ln(1.005^N) To solve for a power, we take the natural log of both sides of the equation. \r
\n" ); document.write( "\n" ); document.write( "ln2=Nln1.005\r
\n" ); document.write( "\n" ); document.write( "N=ln2/ln1.005\r
\n" ); document.write( "\n" ); document.write( "N=.6931/.004987\r
\n" ); document.write( "\n" ); document.write( "N=138.981\r
\n" ); document.write( "\n" ); document.write( "Recall, N is in months, so we divide 138.981/12 to get ANSWER 11.58 years. \r
\n" ); document.write( "\n" ); document.write( "This is 3.3% lower than our guess. The rule of 72 can help you on an exam. For example, if you stopped at N=139 and wrote 139 years, you would know something is wrong. \r
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