An employee accepts a job with a starting salary of 30,000...

An employee accepts a job with a starting salary of $\$ 30,000$ and a cost-of-living increase of $2 \%$ every year for the next 10 years. What is the employee's salary at the start of the $11^{\text {th }}$ year? What are her total earnings during the first 10 years?

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Key Concepts

Compound Growth

Compound growth refers to the process where a quantity increases by a fixed percentage over multiple periods, with each period's increase based on the cumulative total from previous periods. In the context of salary increases, the employee’s salary grows by 2% each year, meaning that the raise each year is calculated based on the salary of the previous year, illustrating the concept of compound growth.

Geometric Sequence

A geometric sequence is an ordered set of numbers where each term is derived by multiplying the previous term by a constant factor, called the common ratio. In scenarios involving salary increases by a fixed percentage, the sequence of annual salaries forms a geometric sequence since each year’s salary is the previous year’s salary multiplied by 1.02.

Geometric Series

A geometric series is the sum of the terms of a geometric sequence. When determining the total earnings over multiple years with annually compounded increases, one sums the series of salaries represented by the geometric sequence. The formula for the sum of a geometric series provides an efficient way to calculate the total earnings over the period.

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