Chapter 12, Problem 38RE

To determine

To find: The salary at the beginning of the fifth year.

Answer to Problem 38RE

The salary as she begins has fifth year will be $\$23,397.1712$

Explanation of Solution

Given information: Your friend has just been hired at an annual salary of $\$20,000$ . She expects to receive annual increases of $4\%$ .

Calculation:

The annual salary is $\$20,000$ .

Since, she expects to receive annual increases of $4\%$ .

Therefore, at the beginning of fifth year, she will get $4$ year increment.

Let’s find the salary at the beginning of fifth year.

Salary at the beginning of second year is

  $\begin{array}{l}=\$20,000+\$20,000\times \frac{4}{100}\\ =\$20,000+\$800\\ =\$20,800\end{array}$

Salary at the beginning of third year is

  $\begin{array}{l}=\$20,800+\$20,800\times \frac{4}{100}\\ =\$20,800+\$832\\ =\$21,632\end{array}$

Salary at the beginning of fourth year is

  $\begin{array}{l}=\$21,632+\$21,632\times \frac{4}{100}\\ =\$21,632+\$865.28\\ =\$22,497.28\end{array}$

Salary at the beginning of fifth year is

  $\begin{array}{l}=\$22,497.28+\$22,497.28\times \frac{4}{100}\\ =\$24,497.28+\$899.8912\\ =\$23,397.1712\end{array}$

Hence, the salary as she begins has fifth year will be $\$23,397.1712$