Question

Zoe started a new job, earning an annual salary of €20000 in her first year. In subsequent years, her salary increased by 2.5% each year.

- Calculate the total amount she will earn in her first 10 years.
I guess I can calculate the salary for each year and then add them. But isn't there a quicker way?

Answer 1

To calculate the total salary Zoe will earn over 10 years, one can use the formula for the sum of a geometric series. Using the initial salary of €20,000 and an annual increase of 2.5%, the formula gives the total accumulated salary over the 10-year period.

Step-by-step explanation:

The question is about calculating the total amount Zoe will earn over 10 years, considering a yearly salary increase of 2.5%. To calculate this faster than adding each year's salary individually, we can use the formula for the sum of a geometric series. Zoe's first-year salary is €20,000, which increases to €20,000 * 1.025 in the second year, and so on. The formula for the total salary over 10 years is:

S = a * [(1 - r^n) / (1 - r)]

Where:

• a is the first term (€20,000)
• r is the common ratio (1.025 for a 2.5% increase)
• n is the number of terms (10 years)

Plugging in the values we get:

S = 20,000 * [(1 - 1.025^10) / (1 - 1.025)]

After calculating, the total amount Zoe will earn in her first 10 years is the sum S.