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The problem provided states:

"A union contract specifies that each worker will receive a 5% pay increase each year for the next 15 years. One worker is paid Php 100,000 the first year. What is this person's total lifetime salary over a 15-year period?"

This is a classic geometric series problem because the salary increases by a constant percentage each year. Let's break it down:

- Initial salary (first year, \( a \)) = Php 100,000
- Annual increase = 5%, which means the salary increases by a factor of \( 1.05 \) each year.
- Number of years (\( n \)) = 15

The total salary over the 15 years can be calculated by summing the salaries for each year. This forms a geometric series, where each term represents the salary for that year.

The formula for the sum \( S \) of the first \( n \) terms of a geometric series is:
\[
S = a \times \frac{1 - r^n}{1 - r}
\]
where:
- \( a \) is the first term (Php 100,000),
- \( r \) is the common ratio (1.05),
- \( n \) is the number of terms (15).

Let me compute this for you.The total lifetime salary of the worker over the 15-year period, considering a 5% annual increase, is approximately **Php 2,157,856.36**.

Would you like a detailed breakdown of the calculation or further assistance? Here are some related questions you might find useful:

1. How is a geometric series different from an arithmetic series?
2. What would the total salary be with a different percentage increase?
3. How much would the salary be in the 10th year?
4. What is the formula for calculating the salary in any specific year?
5. How can you calculate the percentage increase over the entire period?

**Tip**: A geometric series grows exponentially, so even small percentage increases can significantly affect totals over many years.

A union contract specifies that each worker will receive a 5% pay increase each year for the next 15 years. One worker is paid Php 100,000 the first year. What is this person's total lifetime salary over a 15-year period?

Calculate the total lifetime salary of a worker with an initial salary of Php 100,000 and a 5% annual pay increase over 15 years using geometric series. Suitable for high school students in Grades 9-12, covering geometric series and exponential growth.

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