SOLUTION: 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 ba

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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 ba      Log On


   

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?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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?
:
Let x = interest rate in decimal form
:
8000(x+1) = 1st year total
or
8000x + 8000
:
2nd year total
(x+1)(8000 + 8000x + 2500) = 11445
(x+1)(8000x + 10500) = 11445
FOIL
8000x^2 + 10500x + 8000x + 10500 - 11445 = 0
:
A quadratic equation:
8000x^2 + 18500x - 945 = 0
:
simplify divide equation by 5
1600x^2 + 3700x - 189 = 0
:
Use the quadratic formula to solve this:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
a=1600; b=3700, c=-189
x+=+%28-3700+%2B-+sqrt%283700%5E2+-+4+%2A+1600+%2A+-189+%29%29%2F%282%2A1600%29+
x+=+%28-3700+%2B-+sqrt%2813690000+%2B+1209600+%29%29%2F%283200%29+
x+=+%28-3700+%2B-+sqrt%2814899600+%29%29%2F%283200%29+
Positive solution is what we want here:
x+=+%28-3700+%2B+3860%29%2F%283200%29+
x+=+160%2F3200
x = .05, Therefore 5% is the interest rate
;
:
Check solution:
1st year 1.05*8000 = 8400
2nd year 1.05(8400 + 2500) = 11445, confirms our solution