document.write( "Question 642054: determine now much time is required for an investment to double in value if interest is earned at the rate 6.25% compounded monthly
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Algebra.Com's Answer #455180 by FrankM(1040) $\"\"$ $\"About$

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No starting value is required. You are simply asking how many time periods are required to double a value. Here, 6.25% is .5208% per month.
\n" ); document.write( "Before solving, note there is a \"rule of 72.\" A close guess is that 72/6.25 is the years it takes to double. 11.52 years will be close to the answer. \r
\n" ); document.write( "\n" ); document.write( "2=(1.005208^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/ln1.005208\r
\n" ); document.write( "\n" ); document.write( "N=.6931/.0051948\r
\n" ); document.write( "\n" ); document.write( "N=133.4218\r
\n" ); document.write( "\n" ); document.write( "Recall, N is in months, so we divide 133.4218/12 to get ANSWER 11.1188 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=133 and wrote 133 years, you would know something is wrong. \n" ); document.write( "

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