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To solve the problem, let's break it down:

### Given:
- **Initial deposit**: \( X \) RM (unknown)
- **Interest rate**: 8% compounded daily
- **Time periods**:
  - Deposit made on **25 July 2012**.
  - **RM500** withdrawn on **12 August 2012**.
  - Final balance on **31 December 2012** is **RM8,230**.
- We are assuming **360 days per year**.

### Step-by-step solution:
1. **Interest rate**:  
   The daily interest rate is \( \frac{8\%}{360} = \frac{0.08}{360} = 0.0002222 \) (approximately).

2. **Determine the time periods**:
   - From **25 July 2012** to **12 August 2012**, the initial deposit earns interest.  
     Days between: \( 12 - 25 + 31 = 18 \) days.
   - From **12 August 2012** to **31 December 2012**, the remaining amount after withdrawal earns interest.  
     Days between: \( 31 - 12 + 30 + 31 + 30 + 31 + 30 = 140 \) days.

3. **First period (before withdrawal)**:  
   During the first 18 days, the deposit \( X \) earns interest.

   The formula for compound interest is:  
   \[
   A = P \left(1 + \frac{r}{n}\right)^{nt}
   \]
   Where:
   - \( A \) is the amount after interest.
   - \( P \) is the principal (initial amount).
   - \( r \) is the annual interest rate (0.08).
   - \( n \) is the number of times interest is compounded per year (360).
   - \( t \) is the time in years (in this case, days divided by 360).

   After 18 days:
   \[
   A_1 = X \left(1 + \frac{0.08}{360}\right)^{18}
   \]
   Then, **RM500** is withdrawn, so the new balance is:
   \[
   A_2 = A_1 - 500
   \]

4. **Second period (after withdrawal)**:  
   This amount \( A_2 \) will earn interest for 140 days:
   \[
   A_f = A_2 \left(1 + \frac{0.08}{360}\right)^{140}
   \]
   The final amount \( A_f \) is given as RM8,230.

   Now, we can substitute \( A_f = 8230 \), and solve for \( X \).

I'll now calculate the value of \( X \).The initial amount \( X \) that was deposited is approximately **RM8,444.08**.

Would you like more details on this solution or have any other questions?

Here are 5 related questions you might consider:
1. How would the solution change if the interest rate was compounded monthly instead of daily?
2. What would the final balance be if no withdrawal had been made?
3. How is the formula for compound interest derived?
4. How does changing the number of days per year (e.g., using 365 days) affect the result?
5. How would the deposit amount change if the withdrawal had occurred earlier?

**Tip:** When dealing with compound interest problems, carefully check the time intervals and interest compounding frequency, as they significantly affect the calculations.

A sum of money, X ringgit was deposited in a savings account at 8% compounded daily on 25 July 2012. On 12 August 2012, RM500 was withdrawn from the account and the balance as of 31 December 2012 was RM8,230. Find the value of X. (Use exact time and assume 360 days per year)

Learn how to find the initial deposit for a compound interest account where 8% interest is compounded daily, with a withdrawal of RM500 and a final balance of RM8,230. This problem involves key financial concepts like compound interest, daily compounding, and solving for the initial deposit. Suitable for students in Grades 10-12.

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