Let's break down the problem step by step: ### **Given:** - Haley’s highest average annual salary (2021, 2022, 2023): **$1,000,000** - Defined benefit plan: **Pays 3% per year of service** - Benefit is based on the **average of the 3 highest years** of compensation. - **She wants to retire at the beginning of 2024.** - **Find:** - Minimum years of service to maximize the benefit - Annual defined benefit plan payment in 2024 --- ### **Step 1: Maximum Percentage Allowed** Most defined benefit plans have a maximum benefit limit. The problem is suggesting that there is a maximum cap, typically **100% of final average pay**. Since 3% per year × years of service = 100% at 33.33 years, but most plans cap at **30 years** (3% × 30 = 90%), let's check if that's the case. #### **Formula:** \[ \text{Annual Benefit} = \text{Years of Service} \times 3\% \times \text{Average Salary} \] #### **Maximum Years:** \[ \text{Years of service for 100\% benefit} = \frac{100\%}{3\%} = 33.33 \text{ years} \] But plans often cap at **30 years** (for a 90% benefit), as per the hint in your screenshot. --- ### **Step 2: Minimum Number of Years of Service for Maximum Benefit** \[ \text{Maximum benefit with 3% per year} = 3\% \times \text{Years} \] \[ 3\% \times 30 = 90\% \] So, **30 years** is the minimum to get the maximum benefit (since 33.33 years for 100% is usually not allowed). --- ### **Step 3: Annual Defined Benefit Plan Payment (2024)** \[ \text{Annual Payment} = \text{Average Salary} \times \text{Benefit Percentage} \] \[ = \$1,000,000 \times 90\% = \$900,000 \] However, your answer was marked as "not entirely correct." This might be because some plans cap at 100% (33.33 years), so let's check both: #### **If the Plan Caps at 100%:** \[ 33.33 \text{ years} \times 3\% = 100\% \] \[ \$1,000,000 \times 100\% = \$1,000,000 \] #### **If the Plan Caps at 90% (30 years):** \[ \$1,000,000 \times 90\% = \$900,000 \] --- ### **Final Answers:** **If the plan caps at 100%:** - **Minimum number of years of service:** 33.33 years (rounded up to 34 years) - **Annual defined benefit plan payment:** \$1,000,000 **If the plan caps at 90% (which is common):** - **Minimum number of years of service:** 30 years - **Annual defined benefit plan payment:** \$900,000 --- ## **Summary Table** | Minimum number of years of service | Annual defined benefit plan payment | |------------------------------------|-------------------------------------| | 33.33 (or 34) years | $1,000,000 | | 30 years | $900,000 | **Check your plan document for the actual cap (usually 90% or 100%).** **If the answer requires rounding years, use 34 years for 100%, or 30 years for 90%.** --- ### **Explanation** - The minimum years of service to maximize the benefit is determined by the cap on the percentage. - The annual payment is the capped benefit percentage times the average salary. If you have to pick one, **30 years and $900,000** is standard, but check if the plan allows up to 100% (then use 34 years and $1,000,000).

Certainly! Let's carefully analyze the problem again. --- ### **Given Data:** - Haley’s salary in 2021, 2022, and 2023: **$1,000,000** each year - Benefit formula: **3% per year of service** on the **average of the three highest years of compensation** - She plans to retire **at the beginning of 2024** - **Question 1:** Minimum number of years of service to maximize her benefit - **Question 2:** Her annual benefit payment in 2024 if she worked that minimum number of years --- ### **Step 1: Determine the maximum benefit percentage** Since the benefit is 3% per year of service, the maximum benefit (assuming no cap) is: \[ \text{Maximum percentage} = 3\% \times \text{Number of years} \] **Typical plan limits:** Most defined benefit plans cap at **30 years** (corresponding to 90%) or sometimes at **33⅓ years** (100%). --- ### **Step 2: Find the minimum years of service to maximize benefit** - To **maximize her benefit**, she should work **enough years** to reach the **plan's maximum benefit percentage**. - Assuming the plan **caps at 30 years**, then: \[ \text{Benefit percentage} = 3\% \times 30 = 90\% \] - The **minimum number of years** to receive **maximum benefit** is **30 years**. --- ### **Step 3: Calculate her benefit in 2024** - The benefit is based on the **average of her three highest years**, which are all $1,000,000. - Therefore, the **average salary** = $1,000,000. - The **annual benefit payment**: \[ \text{Benefit} = \text{Average salary} \times \text{Benefit percentage} \] - Using 90% (for 30 years): \[ \$1,000,000 \times 0.90 = \$900,000 \] --- ### **Final answers:** | **Minimum years of service** | **Annual benefit payment in 2024** | |------------------------------|----------------------------------| | **30 years** | **$900,000** | --- ### **Note:** - If the plan allows **more than 30 years** (up to 33⅓ years for 100%), then: | **Years of service** | **Benefit percentage** | **Annual benefit** | |----------------------|-------------------------|------------------| | **34 years** (approximate for 100%) | 100% | $1,000,000 | - However, based on typical plan caps, **30 years** is the standard minimum to maximize the benefit. --- ### **Summary:** - **Minimum years of service to maximize benefit:** **30 years** - **Maximum annual benefit in 2024:** **$900,000** --- Let me know if you'd like to explore the scenario with a 100% cap or have further questions!