document.write( "Question 204170: I need help putting this word problem into equation form, can someone help me?\r
\n" ); document.write( "\n" ); document.write( "A business invests $8000 in a savings account for 2 years. At the beginning of the second year, an additional $2500 is invested. At the end of the second year, the account balance is $11445. What was the annual interest rate? \n" ); document.write( "
Algebra.Com's Answer #154138 by ankor@dixie-net.com(22740)\"\" \"About 
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A business invests $8000 in a savings account for 2 years.
\n" ); document.write( " At the beginning of the second year, an additional $2500 is invested.
\n" ); document.write( " At the end of the second year, the account balance is $11445.
\n" ); document.write( " 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( "An equation for this:
\n" ); document.write( ":
\n" ); document.write( "(1+x)((8000(1+x))+2500)) = 11445
\n" ); document.write( ":
\n" ); document.write( "(1+x)(8000 + 8000x + 2500) = 11445
\n" ); document.write( ":
\n" ); document.write( "(1+x)(8000x + 10500) = 11445
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\n" ); document.write( "8000x + 10500 + 8000x^2 + 10500x = 11445
\n" ); document.write( ":
\n" ); document.write( "8000x^2 + 8000x + 10500x + 10500 - 11445 = 0
\n" ); document.write( "Simplify divide by 5:
\n" ); document.write( "8000x^2 + 18500x - 945 = 0
\n" ); document.write( ":
\n" ); document.write( "1600x^2 + 3700x - 189 = 0
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\n" ); document.write( "Use the quadratic formula
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "in this equation: 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( ":
\n" ); document.write( "\"x+=+%28-3700+%2B-+sqrt%2813690000+-+%28-1209600%29+%29%29%2F%283200%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%28-3700+%2B-+sqrt%2813690000+%2B+1209600+%29%29%2F%283200%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%28-3700+%2B-+sqrt%2814899600+%29%29%2F%283200%29+\"
\n" ); document.write( "The positive solution
\n" ); document.write( "\"x+=+%28-3700+%2B+3860%29%2F%283200%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%28160%29%2F%283200%29+\"
\n" ); document.write( "x = .05; 5% is the interest rate
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\n" ); document.write( "See if this is true
\n" ); document.write( "1st year: 1.05*8000 = 8400
\n" ); document.write( "Add 2500 after the 1st year = 10900
\n" ); document.write( "End of 2nd yr: 1.05(10900) = 11445 \n" ); document.write( "
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