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The image you uploaded contains a table for calculating the **future value (F)** and **present value (P)** of simple annuities. The formulas provided in the image are:

1. **Future Value Formula**:
   \[
   F = R \times \frac{(1 + j)^n - 1}{j}
   \]
   
2. **Present Value Formula**:
   \[
   P = R \times \frac{1 - (1 + j)^{-n}}{j}
   \]

Where:
- **R** is the periodic payment,
- **j** is the interest rate per period,
- **n** is the total number of periods.

### Data extracted from the table:
| Payment | Rate | Mode of Payment | Term |
|---------|------|-----------------|------|
| Php 2,500 | 2% | Monthly | 3 years |
| Php 3,000 | 3% | Quarterly | 4 years |
| Php 5,000 | 4% | Quarterly | 5 years |
| Php 7,500 | 5% | Semi-annually | 10 years |
| Php 12,000 | 10% | Annually | 15 years |

Now, let’s calculate the **future value** and **present value** for each case.

### Definitions:
- **Mode of Payment** indicates how often payments are made. For example:
  - Monthly = 12 payments per year,
  - Quarterly = 4 payments per year,
  - Semi-annually = 2 payments per year,
  - Annually = 1 payment per year.
  
- **Rate per period** (**j**) can be calculated by dividing the annual interest rate by the number of payments per year.

- **Number of periods** (**n**) is the total number of payments made over the term. It is calculated as:
  \[
  n = \text{number of payments per year} \times \text{term in years}
  \]

Would you like me to proceed with the calculations for each case?

Find the future value (F) and the present value (P) of the following simple annuities, given the table below.

This problem involves calculating the future value and present value of simple annuities based on different periodic payments, interest rates, and modes of payment. The calculations use standard formulas for future and present values, which are essential for understanding the time value of money in finance.

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