6.1.2 Exam: Semester 2 Exam Question 16 of 40 A college graduate expects to earn a salary of $$ \$ 55,000 $$ during the first year after graduation and receive a $$ 4 \% $$ raise every year after that. What is the total income he will have received after ten years? A. $$ \$ 572,000.00 $$ B. $$ \$ 660,335.89 $$ c. $$ \$ 582,053.74 $$ D. $$ \$ 741,749.33 $$

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UpStudy AI · Accepted Answer

To determine the total income the college graduate will receive over ten years with a starting salary of \$55,000 and a 4% annual raise, we can use the formula for the sum of a geometric series.

**Steps:**

1. **Identify the Variables:**
   - **Initial salary ($$ a $$)**: \$55,000
   - **Annual raise ($$ r $$)**: 4% or 1.04 (as a multiplier)
   - **Number of years ($$ n $$)**: 10

2. **Formula for the Sum of a Geometric Series:**
   $$
   S_n = a \times \frac{r^n - 1}{r - 1}
   $$
   
3. **Calculate $$ r^{10} $$:**
   $$
   1.04^{10} \approx 1.480244
   $$
   
4. **Plug the Values into the Formula:**
   $$
   S_{10} = 55,000 \times \frac{1.480244 - 1}{0.04} = 55,000 \times \frac{0.480244}{0.04} = 55,000 \times 12.0061 \approx 660,335.89
   $$

**Conclusion:**

After performing the calculations, the total income over ten years is approximately **\$660,335.89**.

**Answer:**  
**B. $$ \$ 660,335.89 $$**
The total income after ten years is approximately \$660,335.89. **Answer:** **B. \$660,335.89**

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