A property worth 500,000 appreciates by 12% in the first year and depreciates by 8% in the second year. What is the value at the end of the two years? In a law firm of 60 staff, 35% are qualified lawyers , 25% are paralegals and the rest are administrative staff . How many administrative staff are there? A client pays a 30% deposit on a legal fee of 18,000 . If he later pays half of the outstanding balance,how much does he still owe. A limitation period of 6 years begins on 14th march, 2018, on what date does it expire and how many complete calendar years remain as of 1 January 2023. A court sits 5 days a week for 8 cases per day . At this rate how many weeks will it take to clear a backlog of 480 cases?

Here are the solutions to your questions:

1. Property value calculation

   Step 1: Calculate the value after the first year's appreciation.
   The property appreciates by $12\%$.

   $$\text{Value after 1 year} = 500,000 \times (1 + 0.12)$$ $$\text{Value after 1 year} = 500,000 \times 1.12$$ $$\text{Value after 1 year} = 560,000$$

   Step 2: Calculate the value after the second year's depreciation.
   The property depreciates by $8\%$ from the value at the end of the first year.

   $$\text{Value after 2 years} = 560,000 \times (1 - 0.08)$$ $$\text{Value after 2 years} = 560,000 \times 0.92$$ $$\text{Value after 2 years} = 515,200$$

   The value at the end of the two years is $\boxed{\text{515,200}}$.

2. Administrative staff count

   Step 1: Calculate the total percentage of qualified lawyers and paralegals.

   $$\text{Percentage of lawyers and paralegals} = 35\% + 25\% = 60\%$$

   Step 2: Calculate the percentage of administrative staff.

   $$\text{Percentage of administrative staff} = 100\% - 60\% = 40\%$$

   Step 3: Calculate the number of administrative staff.

   $$\text{Number of administrative staff} = 40\% \text{ of } 60$$ $$\text{Number of administrative staff} = 0.40 \times 60$$ $$\text{Number of administrative staff} = 24$$

   There are $\boxed{\text{24 administrative staff}}$.

3. Outstanding legal fee

   Step 1: Calculate the deposit amount.
   The legal fee is 18,000, and the deposit is $30\%$.

   $$\text{Deposit} = 0.30 \times 18,000$$ $$\text{Deposit} = 5,400$$

   Step 2: Calculate the outstanding balance after the deposit.

   $$\text{Outstanding balance} = 18,000 - 5,400$$ $$\text{Outstanding balance} = 12,600$$

   Step 3: Calculate the amount paid later.
   The client pays half of the outstanding balance.

   $$\text{Amount paid later} = \frac{1}{2} \times 12,600$$ $$\text{Amount paid later} = 6,300$$

   Step 4: Calculate the remaining amount owed.

   $$\text{Amount still owed} = 12,600 - 6,300$$ $$\text{Amount still owed} = 6,300$$

   The client still owes $\boxed{\text{6,300}}$.

4. Limitation period