document.write( "Question 429573: Suppose $500 is invested at 6% annual interest comounded twice a year. When will the investment be worth $1000? And how do you find this answer? \n" ); document.write( "
Algebra.Com's Answer #298352 by stanbon(75887)\"\" \"About 
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Suppose $500 is invested at 6% annual interest comounded twice a year. When will the investment be worth $1000? And how do you find this answer?
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\n" ); document.write( "Formula: A(t) = P(1+(r/n))^(nt)
\n" ); document.write( "where A(t) is the value after t years.
\n" ); document.write( "r is the annual interest rate.
\n" ); document.write( "n is the # of compoundings per year
\n" ); document.write( "t is the # of years.
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\n" ); document.write( "1000 = 500(1+(0.06/2))^(2t)
\n" ); document.write( "2 = (1.03)^(2t)
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\n" ); document.write( "Take the log and solve for \"t\":
\n" ); document.write( "(2t)*log(1.03) = log(2)
\n" ); document.write( "---
\n" ); document.write( "2t = log(2)/log(1.03)
\n" ); document.write( "---
\n" ); document.write( "2t = 23.45
\n" ); document.write( "t = 16.72
\n" ); document.write( "----
\n" ); document.write( "Value will be 1000 sometime during the 16th year.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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