Final answer:
Brenna O'Connor invested $2000 to earn $120 in simple interest over 9 months at an annual interest rate of 8%.
Step-by-step explanation:
To calculate how much money Brenna O'Connor invested to earn $120 in simple interest over 9 months with an annual interest rate of 8%, we can use the simple interest formula:
I = P × r × t
where:
I is the interest earned,
P is the principal amount (initial investment),
r is the annual interest rate (as a decimal), and
t is the time the money is invested (in years).
We're given that Brenna's interest (I) is $120, the annual interest rate (r) is 8% (or 0.08 as a decimal), and the time (t) is 9 months, which is ⅔ or 0.75 years.
Plugging these values into the formula, we get:
120 = P × 0.08 × 0.75
To find P, we divide both sides of the equation by (0.08 × 0.75):
P = 120 / (0.08 × 0.75)
P = $2000
Therefore, Brenna invested $2000 to earn $120 in simple interest.