91Ó°ÊÓ

Use the following information to answer Exercises 14–17. The Merrick Oaks School District offers their employees the following annual pension benefit. $$\begin{array}{|l|}{\text { First } 15 \text { Years of Service }} \\ {2.12 \% \text { multiplier }} \\ {\text { Years of service up to } 15} \\ {\text { Average of final } 3 \text { annual salaries }}\end{array} \begin{array}{l}{\text { Service in Excess of } 15 \text { Years }} \\ {2.25 \% \text { multiplier }} \\ {\text { Years of service in excess of } 15} \\\ {\text { Average of final } 3 \text { annual salaries }}\end{array}$$ Phil is a custodian who has been working for the Merrick Oaks School District for the last 12 years and has decided to retire. His last three years of annual salaries are \(\$ 50,000, \$ 50,000,\) and \(\$ 52,100\) . Determine Phil's annual pension.

Step by step solution

01

Determine Phil's average salary

Since Phil's last three annual salaries were $50,000, $50,000, and $52,100, add these three salaries together and then divide by 3 to find the average: \( \frac{50000+50000+52100} {3} = \$50700 \).

02

Apply the pension benefit

Next, use the multiplier for the first 15 years of service, which is 2.12%, to calculate the pension. Since Phil worked for 12 years, we'll multiply the average salary by the years of service and the multiplier (\(50700 * 0.0212 * 12\)).

03

Calculate the annual pension

Finally, calculate the annual pension by executing the multiplication from the previous step which leads to approximately \$12910.56.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Pension Calculation

Calculating a pension can seem daunting, but it's simply about applying specific rules to determine a regular income for retirees. For Phil, a custodian at the Merrick Oaks School District, the pension is based on a formula that takes into account his years of service and his salary. To calculate a pension, you multiply the average salary by the total years worked and then by a specified percentage, known as a multiplier. This determines the annual pension benefit Phil will receive. It's a way to ensure financial stability in retirement by reflecting both his dedication to his job and his salary history over the last few years.

Salaries Average

The average salary is a key component in calculating pensions because it helps in determining the base amount upon which benefits are derived. For Phil, we need to consider his salaries from the last three years of work: \(\\(50,000 \), \(\\)50,000\), and \(\\(52,100\). We find the average by adding these numbers together and dividing by three:

• Add the salaries: \(50,000 + 50,000 + 52,100 = 152,100\)
• Divide by the number of years: \(\frac{152,100}{3} = 50,700\)

Thus, Phil's average salary used for his pension calculation is \(\\)50,700\). Calculating the average ensures his pension reflects his recent earnings rather than relying on potentially outdated salary figures.

Years of Service

Years of service is crucial in pension calculations as it directly influences the amount an employee can receive after retirement. For employees like Phil in the Merrick Oaks School District, only the first 15 years of service carry a specific multiplier. Phil has 12 years of service, which fits right within the impactful range for his pension calculations. It means each year worked adds to the future pension payout, and each service year has tangible value. The accumulated years determine how the multiplier will be applied to calculate the final pension benefit, making each year worked an important factor for ensuring a sustainable retirement income.

Multipliers Usage

Multipliers play a significant role in adapting the pension calculation to suit different career durations and salary levels. In Phil's situation, for his employment of up to 15 years, the school district uses a 2.12% multiplier. This factor amplifies the effect of his average salary and years worked in determining his pension. Using the calculation:

• Average salary: \(50,700\)
• Years of service: \(12\)
• Multiplier: \(0.0212\) for the first 15 years

The calculation is \(50,700 \times 12 \times 0.0212\), which approximates to an annual pension of \(\$12,910.56\). Here, the multiplier sensitively scales the raw data of salaries and service years into a meaningful pension figure, illustrating its essential role in pension designs and ensuring fairness.