Question: Suppose that you have just been hired at an annual salary of $21,000 and expect to receive annual…

Suppose that you have just been hired at an annual salary of $21,000 and expect to receive annual increases of 4%. What will your salary be when you begin your fifth year?

Solution

To find your salary at the beginning of the fifth year, we will calculate the salary increase over the first four years. Start with the initial salary \( S_0 \) at year 0: \[ S_0 = 21000 \] Calculate the salary at the beginning of each year using the formula \( S_n = S_{n-1} \times (1 + r) \), where \( r = 0.04 \) is the 4% increase rate. At the beginning of the first year: \[ S_1 = S_0 \times 1.04 \] \[ S_1 = 21000 \times 1.04 \] \[ S_1 = 21840 \] At the beginning of the second year: \[ S_2 = S_1 \times 1.04 \] \[ S_2 = 21840 \times 1.04 \] \[ S_2 = 22713.6 \] At the beginning of the third year: \[ S_3 = S_2 \times 1.04 \] \[ S_3 = 22713.6 \times 1.04 \] \[ S_3 = 23622.144 \] At the beginning of the fourth year: \[ S_4 = S_3 \times 1.04 \] \[ S_4 = 23622.144 \times 1.04 \] \[ S_4 = 24566.02976 \] Therefore, the salary at the beginning of the fifth year is approximately $24,566.03.