Final answer:
To find the interest rate for a $9000 deposit accumulating to $10,450.66, compounded quarterly for 5 years, you can use the formula A = P(1 + r/n)^(nt). In this case, the interest rate is approximately 7.2%.
Step-by-step explanation:
To find the interest rate for a $9000 deposit accumulating to $10,450.66, compounded quarterly for 5 years, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, A = $10,450.66, P = $9000, n = 4 (quarterly compounding), and t = 5. Substituting these values into the formula, we get:
$10,450.66 = $9000(1 + r/4)^(4*5)
Dividing both sides of the equation by $9000, we have:
1.161185 ≈ (1 + r/4)^20
Taking the 20th root of both sides, we get:
1 + r/4 ≈ 1.018
Subtracting 1 from both sides, we have:
r/4 ≈ 0.018
Multiplying both sides by 4, we get:
r ≈ 0.072 or 7.2%
The interest rate for this deposit is approximately 7.2%.