document.write( "Question 895873: . The Tanners have received an $8000 gift from one of their parents to invest in their child’s college education. They estimate that they will need $20,000 in 12 years to achieve their educational goals for their child. What interest rate compounded semiannually would the Tanners need to achieve this goal?
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Algebra.Com's Answer #543222 by lwsshak3(11628)\"\" \"About 
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The Tanners have received an $8000 gift from one of their parents to invest in their child’s college education. They estimate that they will need $20,000 in 12 years to achieve their educational goals for their child. What interest rate compounded semiannually would the Tanners need to achieve this goal?
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\n" ); document.write( "Compound interest formula:
\n" ); document.write( "A=P(1+i)^n, P=initial investment, i=interest rate per compounding period, n=number of periods, A=amount after n-periods
\n" ); document.write( "..
\n" ); document.write( "For given problem:
\n" ); document.write( "P=8000
\n" ); document.write( "n=2*12=24 compounding perods
\n" ); document.write( "A=12000
\n" ); document.write( "..
\n" ); document.write( "A/P=(1+i)^24
\n" ); document.write( "12000/8000=(1+i)^24
\n" ); document.write( "1.5=(1+i)^24
\n" ); document.write( "take log of both sides
\n" ); document.write( "log1.5=24log(1+i)
\n" ); document.write( "log1.5/24=log(1+i)
\n" ); document.write( ".007337=log(1+i)
\n" ); document.write( "10^(.007337)=1+i
\n" ); document.write( "1+i=1.017
\n" ); document.write( "i=1.017-1=.017 (interest rate per compounding period)
\n" ); document.write( "annual interest rate=2*.017=.034 or 3.4% \n" ); document.write( "
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