document.write( "Question 180501: A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?
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Algebra.Com's Answer #135418 by ankor@dixie-net.com(22740)\"\" \"About 
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A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?
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\n" ); document.write( "Let x = interest rate in decimal form
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\n" ); document.write( "8000(x+1) = 1st year total
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\n" ); document.write( "8000x + 8000
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\n" ); document.write( "2nd year total
\n" ); document.write( "(x+1)(8000 + 8000x + 2500) = 11445
\n" ); document.write( "(x+1)(8000x + 10500) = 11445
\n" ); document.write( "FOIL
\n" ); document.write( "8000x^2 + 10500x + 8000x + 10500 - 11445 = 0
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\n" ); document.write( "A quadratic equation:
\n" ); document.write( "8000x^2 + 18500x - 945 = 0
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\n" ); document.write( "simplify divide equation by 5
\n" ); document.write( "1600x^2 + 3700x - 189 = 0
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\n" ); document.write( "Use the quadratic formula to solve this:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
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\n" ); document.write( "a=1600; b=3700, c=-189
\n" ); document.write( "\"x+=+%28-3700+%2B-+sqrt%283700%5E2+-+4+%2A+1600+%2A+-189+%29%29%2F%282%2A1600%29+\"
\n" ); document.write( "\"x+=+%28-3700+%2B-+sqrt%2813690000+%2B+1209600+%29%29%2F%283200%29+\"
\n" ); document.write( "\"x+=+%28-3700+%2B-+sqrt%2814899600+%29%29%2F%283200%29+\"
\n" ); document.write( "Positive solution is what we want here:
\n" ); document.write( "\"x+=+%28-3700+%2B+3860%29%2F%283200%29+\"
\n" ); document.write( "\"x+=+160%2F3200\"
\n" ); document.write( "x = .05, Therefore 5% is the interest rate
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\n" ); document.write( "Check solution:
\n" ); document.write( "1st year 1.05*8000 = 8400
\n" ); document.write( "2nd year 1.05(8400 + 2500) = 11445, confirms our solution
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