document.write( "Question 38464: Could you please explain how the rule of 72 works. I understand that it is an easy way to figure out how many years it would take to double your money, but I get very confused about why it works. How do I use a logrithm to solve it? I just don't understand logs at all. I know that they are exponents, right? I'm lost \n" ); document.write( "
Algebra.Com's Answer #23990 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
If P amount of money is compounded continuously the
\n" ); document.write( "amount (A) of money you will get is as follows:
\n" ); document.write( "A=Pe^rt where r is the annual interest rate and t is the number
\n" ); document.write( "of years you allow the compounded to go on.\r
\n" ); document.write( "\n" ); document.write( "Your problem is to find \"t\" so that A will equal 2P, i.e.
\n" ); document.write( "P will double.
\n" ); document.write( "So, 2P=Pe^rt
\n" ); document.write( "Divide both sides by P to get;
\n" ); document.write( "2 =e^rt
\n" ); document.write( "Take the natural logarithm of both sides to get
\n" ); document.write( "ln2 = rt
\n" ); document.write( "t = (1/r)ln2= (1/r)(0.69314718...)
\n" ); document.write( "If t = 7 then
\n" ); document.write( " r=0.69314718...
\n" ); document.write( " r is approximately 10%
\n" ); document.write( "All of this says that money will double in value
\n" ); document.write( "every 7 years if invested in a continuously
\n" ); document.write( "compounding account at 10% annual interest.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( " \n" ); document.write( "
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