Question

question 1-8
grayson deposited $4,500 into a new account.

• the account earned annual simple interest.
• no withdrawals or deposits were made.
• at the end of 2 years, the balance of the account was $5,265.

what is the annual interest rate on this account?
□ 5.2%
□ 8.5%
□ 7.3%
□ 4.7%

Explanation:

Step1: Recall simple interest formula

The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. The total balance $A$ is $A = P + I$, so $I = A - P$.

First, find the interest earned. $P = 4500$, $A = 5265$, so $I = 5265 - 4500 = 765$.

Step2: Substitute into interest formula

We know $I = 765$, $P = 4500$, $t = 2$. Substitute into $I = P \times r \times t$:

$765 = 4500 \times r \times 2$

Simplify the right side: $4500 \times 2 = 9000$, so $765 = 9000r$

Step3: Solve for r

Divide both sides by 9000: $r = \frac{765}{9000} = 0.085$

Convert to percentage: $0.085 \times 100 = 8.5\%$

Answer:

8.5% (corresponding to the option with 8.5%)