SOLUTION: please help me out with this problem 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 th

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: please help me out with this problem 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 th      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 172637This question is from textbook
: please help me out with this problem
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? This question is from textbook

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
2.10000(x+1)(x+1)+3500(x+1)=15569.75------>where x is the interest rate
.... dealing with a quadratic formula.....
when you solve this email me and I will let you know if you have the correct answer.
10000%28x%5E2%2B2x%2B1%29%2B3500x%2B3500=15569.75
:
10000x%5E2%2B20000x%2B10000%2B3500x%2B3500=15569.75
:
10000x%5E2%2B23500x-2069.75=0
:
drop the negative valuesystem%28x=.085%2Cx=-2.64%29
:
highlight%28x=.085%29or 8.5%
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 10000x%5E2%2B23500x%2B-2069+=+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=635010000.

Discriminant d=635010000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-23500%2B-sqrt%28+635010000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2823500%29%2Bsqrt%28+635010000+%29%29%2F2%5C10000+=+0.0849702377437334
x%5B2%5D+=+%28-%2823500%29-sqrt%28+635010000+%29%29%2F2%5C10000+=+-2.43497023774373

Quadratic expression 10000x%5E2%2B23500x%2B-2069 can be factored:
10000x%5E2%2B23500x%2B-2069+=+10000%28x-0.0849702377437334%29%2A%28x--2.43497023774373%29
Again, the answer is: 0.0849702377437334, -2.43497023774373. 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+%29