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

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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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=635040000 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.085, -2.435. Here's your graph:
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