Salary increase 2

Each year, Francesca earns a salary 2 percent higher than her previous year's salary. In her first five years at this job, she earned a total of $187,345. What was Francesca's salary in her 1st year at this job?

Correct answer:

a =  36000 USD

Step-by-step explanation:

$$\begin{gathered} q=100\%+2\%=1+\frac{2}{100}=1.02 \\ s=187345\text{USD} \\ a+q\cdot a+q^2\cdot a+q^3\cdot a+q^4\cdot a=s \\ a(1+q+q^2+q^3+q^4)=s \\ a=\frac{s}{1+q+q^2+q^3+q^4} \\ r=1+q+q^2+q^3+q^4=1+\frac{51}{50}+{\frac{51}{50}}^2+{\frac{51}{50}}^3+{\frac{51}{50}}^4\doteq 5.204 \\ a=\frac{s}{r}=\frac{187345}{r}=\frac{187345}{5.204}=36000\text{USD} \end{gathered}$$

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