To solve the problem:

Keegan earns 3% simple interest on her deposit. Her final account balance is $360.50 at the end of the year. Let $P$ represent the initial deposit. Using the simple interest formula:

$A = P + (P \cdot r \cdot t)$

Where:

• $A$ is the final amount = $360.50,
• $P$ is the initial deposit (unknown),
• $r$ is the interest rate = 0.03,
• $t$ is the time in years = 1.

Simplify the formula:

$360.50 = P + (P \cdot 0.03 \cdot 1)$

$360.50 = P(1 + 0.03)$

$360.50 = P(1.03)$

Solve for $P$:

$P = \frac{360.50}{1.03}$

$P \approx 350.00$

So, Keegan deposited $350.00 at the beginning of the year.

Let me know if you want a detailed breakdown or have any questions!

Expanding Questions:

1. What is the formula for calculating compound interest?
2. How does the time period affect the simple interest earned?
3. What are the differences between simple and compound interest?
4. Can simple interest ever exceed the principal amount in a fixed time?
5. How would the calculation change if Keegan made deposits during the year?

Tip:

Always double-check whether the question specifies simple or compound interest, as it significantly affects the calculation!