SOLUTION: A business invests $10,000 in a savings account for two years. At the beginning of the second year, an additional $3500 is invested. At the end of the second year, the account ba

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A business invests $10,000 in a savings account for two years. At the beginning of the second year, an additional $3500 is invested. At the end of the second year, the account ba      Log On


   



Question 114094: A business invests $10,000 in a savings account for two years. At the beginning of the second year, an additional $3500 is invested. At the end of the second year, the account balance is $15,569.75. What was the annual interest rate?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the annual interest rate.
10000+10000x= total amount after 1yr.
x(13500+10000x)+13500+10000x=15569.75
13500x+10000x^2+13500+10000x-15569.75=0
10000x^2+23500x-2069.75=0
x=-2.435, x=.085 (see below)
x=.085 is the only answer for this question because the other is negative.
Annual interest rate is 8.5%
Ed
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 10000x%5E2%2B23500x%2B-2069.75+=+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=%2823500%29%5E2-4%2A10000%2A-2069.75=635040000.

Discriminant d=635040000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-23500%2B-sqrt%28+635040000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2823500%29%2Bsqrt%28+635040000+%29%29%2F2%5C10000+=+0.085
x%5B2%5D+=+%28-%2823500%29-sqrt%28+635040000+%29%29%2F2%5C10000+=+-2.435

Quadratic expression 10000x%5E2%2B23500x%2B-2069.75 can be factored:
10000x%5E2%2B23500x%2B-2069.75+=+%28x-0.085%29%2A%28x--2.435%29
Again, the answer is: 0.085, -2.435. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10000%2Ax%5E2%2B23500%2Ax%2B-2069.75+%29