SOLUTION: Clara earned \$360 in simple interest on a 12-month bank certificate of deposit. If the interest rate had been 3% higher, she would have earned the same amount of money by depositin

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Question 57493: Clara earned \$360 in simple interest on a 12-month bank certificate of deposit. If the interest rate had been 3% higher, she would have earned the same amount of money by depositing \$1,000 less. How much money did Clara deposit, and what was her interest rate?

Answer by hayek(51)   (Show Source):
You can put this solution on YOUR website!
Simple interest formula is Interest = (Deposit Amt. (P)) * (Interest Rate (i))
(I use P as the Deposit Amount as this is often call the Principal Amount)
The problems tells us Clara earned \$360 in interest.
The problem also tells us if the interest were 3% more (i.e. i+0.03), she would have earned the same amount (360) if she deposited 1,000 less (i.e. (P-1000)).
Thus, we have the following two formulas:
(Eq. 1)
(Eq. 2)
Solve Eq.1 for P:
(Eq. 3)
Plug the Eq.3 result into Eq. 2:

Now, distribute:

Multiply both sides by i:

Solving using the quadratic formula gives two solutions: i=.09, -.12.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=44100 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.09, -0.12. Here's your graph:

So, Clara's interest rate (i) was 9%.
Plug that into Eq.1 to get her total deposit: 360=p(.09)
P=\$4000