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 balan

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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 balan      Log On


   

Question 180563: 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 Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
assuming the interest rate is the same for both amounts invested
:
8000%2B8000x%2B%288000%2B8000x%29x%2B2500%2B2500x=11445
:
8000%2B8000x%2B8000x%2B8000x%5E2%2B2500%2B2500x=11445
:
8000x%5E2%2B18500x-945=0
:
x=.05 and -2.36
:
throw out the negative
:
interest rate is .05%28100%29=highlight%285%29%
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8000x%5E2%2B18500x%2B-945+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2818500%29%5E2-4%2A8000%2A-945=372490000.

Discriminant d=372490000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18500%2B-sqrt%28+372490000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818500%29%2Bsqrt%28+372490000+%29%29%2F2%5C8000+=+0.05
x%5B2%5D+=+%28-%2818500%29-sqrt%28+372490000+%29%29%2F2%5C8000+=+-2.3625

Quadratic expression 8000x%5E2%2B18500x%2B-945 can be factored:
8000x%5E2%2B18500x%2B-945+=+%28x-0.05%29%2A%28x--2.3625%29
Again, the answer is: 0.05, -2.3625. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8000%2Ax%5E2%2B18500%2Ax%2B-945+%29