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The image contains a table with financial values for calculating interest, with columns labeled \( P \) (Principal), \( r \) (Rate), \( t \) (Time), \( i \) (Interest), and \( F \) (Future Value). The task is to complete the table based on the given information.

### The formulae used are:

- **Interest**: 
  \[
  i = P \times r \times t
  \]
  where \( r \) is the interest rate per year (expressed as a decimal), and \( t \) is the time in years.
  
- **Future Value**: 
  \[
  F = P + i
  \]

### Let's fill in the blanks using the provided dataThe image contains a table with financial values for calculating interest, with columns labeled \( P \) (Principal), \( r \) (Rate), \( t \) (Time), \( i \) (Interest), and \( F \) (Future Value). The task is to complete the table based on the given information.

### The formulae used are:

- **Interest**: 
  \[
  i = P \times r \times t
  \]
  where \( r \) is the interest rate per year (expressed as a decimal), and \( t \) is the time in years.
  
- **Future Value**: 
  \[
  F = P + i
  \]

### Let's fill in the blanks using the provided 

1. **Row 1:**
   - \( P = 25,250 \)
   - \( r = 6.25\% = 0.0625 \)
   - \( t = 4 \, \text{years} \)
   - **Given Interest** \( i = 6,317.50 \)
   - **Future Value** \( F = 31,567.50 \)
   (These values are provided.)

2. **Row 2:**
   - \( P = 12,725 \)
   - \( r = 2.09\% = 0.0209 \)
   - \( t = 2.5 \, \text{years} \)
   - **Interest** \( i = P \times r \times t = 12,725 \times 0.0209 \times 2.5 = 665.03 \)
   - **Future Value** \( F = P + i = 12,725 + 665.03 = 13,390.03 \)

3. **Row 3:**
   - \( P = 23,155 \)
   - \( r = 4.5\% = 0.045 \)
   - \( t = 1 \, \text{year} + 5 \, \text{months} = 1 + \frac{5}{12} \approx 1.42 \, \text{years} \)
   - **Given Interest** \( i = 1,500 \)
   - **Future Value** \( F = P + i = 23,155 + 1,500 = 24,655 \)

4. **Row 4:**
   - \( P = 27,675 \)
   - \( r = 5\% = 0.05 \)
   - \( t = 5 \, \text{years} + 9 \, \text{months} = 5 + \frac{9}{12} = 5.75 \, \text{years} \)
   - **Given Future Value** \( F = 35,000 \)
   - **Interest** \( i = F - P = 35,000 - 27,675 = 7,325 \)

5. **Row 5:**
   - \( P = 12,568 \)
   - \( r = 3\frac{1}{8}\% = 3.125\% = 0.03125 \)
   - \( t = 2 \, \text{years} \)
   - **Interest** \( i = P \times r \times t = 12,568 \times 0.03125 \times 2 = 785.5 \)
   - **Future Value** \( F = P + i = 12,568 + 785.5 = 13,353.5 \)

### Completed Table:

| D (P)  | r         | t           | i         | F           |
|--------|-----------|-------------|-----------|-------------|
| 25,250 | 6.25%     | 4 years     | 6,317.50  | 31,567.50   |
| 12,725 | 2.09%     | 2.5 years   | 665.03    | 13,390.03   |
| 23,155 | 4.5%      | 1 year 5 mos| 1,500     | 24,655      |
| 27,675 | 5%        | 5 years 9 mos| 7,325     | 35,000      |
| 12,568 | 3.125%    | 2 years     | 785.50    | 13,353.50   |

Do you have any questions or need further details? Here are some relative questions to explore further:

1. How would you calculate the future value for compound interest scenarios?
2. What impact does an increase in the interest rate have on the future value?
3. How does converting months into years affect the time calculation?
4. What is the difference between simple and compound interest?
5. How would the future value change if the time period increased?

**Tip**: Always express percentages as decimals when using formulas for interest calculations!

Complete the table based on the provided financial values using the simple interest formula.

Learn how to calculate simple interest and future value for given principal amounts, interest rates, and time periods. This problem explores financial mathematics concepts, using the formulas i = P × r × t and F = P + i. Suitable for Grades 9-12.

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