Algebra.Com's Answer #853876 by ikleyn(53742)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
.
\n" );
document.write( "A commonly asked question is, \"How long will it take to double my money?\" At 10% interest rate and
\n" );
document.write( "continuous compounding, what is the answer?
\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " The solution in the post by the other tutor is fatally incorrect.\r
\n" );
document.write( "\n" );
document.write( " I came to bring a correct solution.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "The formula for the future value at continuous compounding is \r\n" );
document.write( "\r\n" );
document.write( " FV =  , (1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where A is the deposited amount, 'r' is the nominal interest rate and 't' is the time in years,\r\n" );
document.write( "'e' is the base of natural logarithms (e = 2.71828...)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In your problem, A = 10,000 dollars, FV= 20,000 dollars, r = 0.1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, formula (1) takes the form\r\n" );
document.write( "\r\n" );
document.write( " 20000 =  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies\r\n" );
document.write( "\r\n" );
document.write( "  =  ,\r\n" );
document.write( "\r\n" );
document.write( " 2 = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Take natural logarithm of both sides \r\n" );
document.write( "\r\n" );
document.write( " ln(2) = 0.1*t\r\n" );
document.write( "\r\n" );
document.write( " t =  = 6.93147 years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWEWR. The time to double the deposited amount is about 6.93 years under given conditions.\r\n" );
document.write( " \r
\n" );
document.write( "\n" );
document.write( "Solved correctly with complete explanations.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |