Question

marla earns an annual salary of $28,000 at her new job. She received a 3% salary increase every year. Find Marla’s total earnings over the course of her first five years working at her job.

Answer 1

ANSWER:

$148,655.8

STEP-BY-STEP EXPLANATION:

Given:

Original salary = $28,000

Increase per year = 3%

The sum of all the earnings would be the sum of the original salary, the salary after 1 year, the salary after 2 years, the salary after 3 years and the salary after 4 years.

The salary in each year is calculated by multiplying the original salary by the increase raised after n years, just like this:

$\begin{gathered} s_n=28000\cdot(1+3\%)^n_{} \\ s_n=28000\cdot(1+0.03)^n_{} \\ s_n=28000\cdot(1.03)^n_{} \end{gathered}$

Therefore, the total earnings would be as follows:

$\begin{gathered} t=28000+28000\cdot(1.03)^1+28000\cdot(1.03)^2+28000\cdot(1.03)^3+28000\cdot(1.03)^4 \\ t=28000+28840+29705.2+30596.4+31514.2 \\ t=148655.8 \end{gathered}$

Therefore, the earnings in the first 5 years of MARla is $148,655.8