document.write( "Question 494471: How long does it take to double an investment of $1,000 in an amount that pays 8% annual interest rate if: \r
\n" ); document.write( "\n" ); document.write( "1. Interest is compounded quarterly?
\n" ); document.write( "2. Interest is compounded continuously? \n" ); document.write( "
Algebra.Com's Answer #335669 by Alan3354(69443)\"\" \"About 
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How long does it take to double an investment of $1,000 in an amount that pays 8% annual interest rate if:\r
\n" ); document.write( "\n" ); document.write( "1. Interest is compounded quarterly?
\n" ); document.write( "8% annual = 2% per quarter
\n" ); document.write( "FV = PV*(1 + 0.02)^n
\n" ); document.write( "2 = (1.02)^n the amount is irrelevant, any amount will be doubled.
\n" ); document.write( "log(2) = n*log(1.02)
\n" ); document.write( "n = log(2)/log(1.02)
\n" ); document.write( "n =~ 35.003 quarters
\n" ); document.write( "You can use logs or ln, natural logs, same result
\n" ); document.write( "----------------------
\n" ); document.write( "2. Interest is compounded continuously?
\n" ); document.write( "FV = PV*e^rt = PV*e^0.08t
\n" ); document.write( "2 = e^0.08t
\n" ); document.write( "ln(2) = 0.08t
\n" ); document.write( "t = ln(2)/0.08
\n" ); document.write( "t =~ 8.66434 years
\n" ); document.write( "= 34.66 quarters
\n" ); document.write( "Not much difference \n" ); document.write( "
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