document.write( "Question 864443: How long will it take $5000, invested at 7% interest compounded quarterly, to reach a value of $17,000? \n" ); document.write( "

Algebra.Com's Answer #521038 by LinnW(1048) $\"\"$ $\"About$

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At 7% per year, the quarterly compounding amount is 0.07/4 = 0.0175
\n" ); document.write( "Set x = the number of quarters required to end up with $17,000
\n" ); document.write( "So 5000*(1.0175^x) = 17000
\n" ); document.write( "divide each side by 5000
\n" ); document.write( "1.0175^x = 17000/5000
\n" ); document.write( "1.0175^x = 3.4
\n" ); document.write( "Take the log of each side
\n" ); document.write( "log(1.0175^x) = log(3.4)
\n" ); document.write( "x*log(1.0175) = log(3.4)
\n" ); document.write( "divide each side by log(1.0175)
\n" ); document.write( "x = $\"log%283.4%29%2Flog%281.0175%29\"$
\n" ); document.write( "x = approximately 70.540143
\n" ); document.write( "So 5000*(1.0175^70.540143) should be close to 17,000
\n" ); document.write( "So in just a little over 70 quarters or just over 17.5 years,
\n" ); document.write( "5000 becomes 17000 \n" ); document.write( "

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