Question

Your friend has just been hired at an annual salary of $20,000. If she expects to receive annual increases of 4%, what will be her salary as she begins her fifth year .

Short answer

The salary in the fifth year is approximately$\$23,397$.

Step-by-step solution

Step 1. Given information

The initial salary is $20,000.

The annual increase in salary is 4%.

Step 2. To find salary in the fifth year.

In first-year salary is: $a_1=20,000$

In the second year, the salary will be

$a_2=20,000\times 1.04$

In the third year, the salary will be

$$\begin{gathered} a_3=20,000\times 1.04\times 1.04 \\ =20,000{(1.04)}^2 \end{gathered}$$

In the fourth year, the salary will be

$a_4=20,000{(1.04)}^3$

In the fourth year, the salary will be

$$\begin{gathered} a_5=20,000{(1.04)}^4=20,000\times 1.17 \\ \approx 23,397 \end{gathered}$$