Question 57493
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:

{{{360=P*i}}} (Eq. 1)
{{{360=(P-1000)*(i+.03)}}} (Eq. 2)

Solve Eq.1 for P: 
{{{P=360/i}}} (Eq. 3)
Plug the Eq.3 result into Eq. 2: 
{{{360=((360/i)-1000)*(i+.03)}}}
Now, distribute:
{{{360=(360/i)(i)+(360/i)(0.03)-1000i-1000(.03)}}}
{{{360=360+10.8/i-1000i-30}}}
{{{0=10.8/i-1000i-30}}}
Multiply both sides by i:
{{{0=10.8-1000i^2-30i}}}
{{{1000i^2+30i-10.8=0}}}
Solving using the quadratic formula gives two solutions: i=.09, -.12.
*[invoke quadratic "i", 1000, 30, -10.8]

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