Madison was offered a job that paid a salary of dollar sign, 73, comma, 000$73,000 in its first year. The salary was set to increase by 1% per year every year. If Madison worked at the job for 21 years, what was the *total* amount of money earned over the 21 years, *to the nearest whole number*?

Madison's salary increases by 1% each year, meaning this is a geometric series problem. The salary in the first year is $73,000, and each subsequent year's salary is 1% higher than the previous year.

### Step 1: Formula for the Total Amount Earned

We can use the formula for the sum of a geometric series:

\[
S_n = a \frac{1 - r^n}{1 - r}
\]

Where:
- $S_n$ is the total sum of the salaries over 21 years,
- $a$ is the initial salary ($73,000),
- $r$ is the common ratio (1 + 1% = 1.01),
- $n$ is the number of years (21 years).

### Step 2: Substitute the values

\[
S_{21} = 73,000 \times \frac{1 - 1.01^{21}}{1 - 1.01}
\]

Let's calculate this value.Madison earned a total of \$1,696,461 over the 21 years, rounded to the nearest whole number.

Would you like more details on any of the steps? Here are 5 related questions to deepen your understanding:

1. How would the total change if the salary increased by 2% annually?
2. What is the total amount Madison earned after 10 years?
3. Can the same geometric series formula be applied if the salary decreased by a certain percentage each year?
4. How can this problem be modeled graphically over time?
5. What is the total salary earned in the 21st year alone?

**Tip:** Geometric series are often used to model scenarios involving steady percentage growth, like salary increments or compound interest.

Madison was offered a job that paid a salary of $73,000 in its first year. The salary was set to increase by 1% per year every year. If Madison worked at the job for 21 years, what was the total amount of money earned over the 21 years, to the nearest whole number?

Discover how to calculate the total salary Madison earned over 21 years, starting at $73,000 with a 1% annual increase. This problem involves geometric series, a key algebraic concept, and is ideal for high school students studying percentage growth and series summation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation