Let's break down the problem: **Given:** - Haley's annual salary for 2021, 2022, and 2023 = **$1,000,000** each year. - Defined benefit plan pays **3% for every year of service** for the average of her three highest years of compensation. - She is retiring at the beginning of 2024. - **Question:** What is the **minimum number of years of service** to maximize the benefit? What is the **annual defined benefit plan payment** in 2024? --- ### **Step 1: Understanding Plan Maximum** Defined benefit plans usually **cap the maximum benefit**. The most common cap is **100% of final/highest average salary** or a maximum number of years (often 30 to 35 years). If the plan pays 3% per year, then: - To reach 100%, you need: \( \frac{100}{3} = 33.33 \) years (so, typically capped at 33⅓ years). - However, many plans cap at **30 years** (since 3% × 30 = 90%). But the question specifically asks for the **minimum number of years to receive the maximum benefit** (often the cap is 100% of salary). --- ### **Step 2: Calculate the Years Needed for Maximum Benefit** - Each year = 3% - To get **100%**, need \( \frac{100}{3} = 33.33 \) years - **Minimum number of years to maximize benefit = 34 years** (since you can't have a fraction of a year and must round up). --- ### **Step 3: Calculate the Average of Highest 3 Years' Salary** - 2021: $1,000,000 - 2022: $1,000,000 - 2023: $1,000,000 **Average = \(\frac{1,000,000 + 1,000,000 + 1,000,000}{3} = $1,000,000\)** --- ### **Step 4: Calculate the Payment** - **If maximum years is 34:** \( 34 \times 3\% = 102\% \) - Most plans cap at 100%, so **maximum payment = 100% \times $1,000,000 = $1,000,000** --- ## **Final Answers** | | Answer | |---------------------------|-------------| | Minimum number of years of service | **34 years** | | Payment under annual defined benefit plan | **$1,000,000** | --- ### **Explanation of Previous Answer's Error** - **30 years** only gives 90% of salary ($900,000), **not the maximum**. - The **minimum years to reach 100%** is 34 years (since 33.33 rounds up). --- ## **Summary Table** | Item | Correct Answer | |----------------------------------------------|------------------------| | Minimum number of years of service | 34 years | | Payment under annual defined benefit plan | $1,000,000 | Let me know if you need any clarification!

Let's carefully analyze the problem step-by-step to determine the correct answers. --- ### Given Data: - Haley's salary for 2021, 2022, and 2023 = **$1,000,000** each year. - The plan pays **3%** for each year of service based on the **average of her three highest years of compensation**. - She plans to retire **at the beginning of 2024**. - **Question 1:** What is the **minimum number of years of service** to **maximize her benefit**? - **Question 2:** If she works that minimum number of years, what is her **annual benefit payment** in 2024? --- ### Step 1: Determine the maximum benefit percentage Each year of service adds **3%**, so: - **Maximum benefit percentage = 3% × number of years of service**. - Generally, benefit caps occur at **100%** of the average salary. --- ### Step 2: Find the minimum number of years to reach maximum benefit - To get **100%** of her highest three-year average salary: \[ 3\% \times \text{years of service} = 100\% \] \[ \text{years of service} = \frac{100\%}{3\%} \approx 33.33 \text{ years} \] - Since she cannot work a fraction of a year, she must work **at least 34 years** to **reach or exceed 100%**. **Therefore, the minimum number of years of service to maximize her benefit is:** **Answer: 34 years** --- ### Step 3: Calculate her benefit amount - Her **average of the three highest years** of salary is: \[ \frac{2021 + 2022 + 2023}{3} = \frac{\$1,000,000 + \$1,000,000 + \$1,000,000}{3} = \$1,000,000 \] - The **benefit percentage** at 34 years: \[ 3\% \times 34 = 102\% \] - Since plan benefits are typically capped at **100%** of the average salary, **her maximum benefit** would be: \[ 100\% \times \$1,000,000 = \$1,000,000 \] --- ### **Final answers:** | **Question** | **Answer** | |----------------|--------------------------------------------------------| | Minimum years of service to maximize benefit | **34 years** | | Annual benefit payment in 2024 (assuming maximum benefit) | **$1,000,000** | --- ### **Summary:** - To fully maximize her benefit (i.e., reach 100%), Haley needs **at least 34 years** of service. - Her **annual benefit payment** at retirement would be **$1,000,000**. --- If you'd like any further clarification, feel free to ask!