/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 Sara works for the City of North... [FREE SOLUTION] | 91Ó°ÊÓ

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Sara works for the City of Northbeck. The city calculates an employee's pension according to the following formula. \(\bullet\) Determine the average of the highest 3 years of annual earnings. \(\bullet\) Determine the monthly average using the above amount. \(\bullet\) Subtract \(\$ 600\) from that amount. \(\bullet\) Multiply the result by 30\(\% .\) \(\bullet\) Add \(\$ 400\) to that result. \(\bullet\) For each year of employment over 15 years, add 1\(\%\) of the average monthly salary, not to exceed \(\$ 100\) for each year. \(\bullet\) The final result is the monthly pension benefit. Sara's three highest annual salaries are \(\$ 90,000, \$ 92,598,\) and \(\$ 93,000\) . Calculate Sara's monthly pension benefit to the nearest penny if she retires after 18 years of employment.

Short Answer

Expert verified
Sara's monthly pension benefit, if she retires after 18 years of employment, will be \$2,592.16.

Step by step solution

01

Calculate Average Annual Salary

The first step is to find the average of Sara's highest three salary years. The salaries given are $90,000, $92,598, and $93,000. The average of these values can be calculated by adding them and dividing by 3, i.e. \((\$90,000 + \$92,598 + \$93,000)/3 \). This gives an average of \$91,866.
02

Calculate Monthly Average Salary

Now, let's find the monthly average of the annual salary. We need to divide our average annual salary by 12. This is \$91,866/12 which gives a monthly average of \$7,655.50.
03

Subtract Constant Amount

Next, subtract \$600 from the monthly average salary, i.e. \$7,655.50 - \$600. This gives \$7,055.50.
04

Pension Base Calculation

Now, the next step in the formula is to multiply this result by 30\%. To do this multiply \$7,055.50 by 0.30, giving \$2,116.65.
05

Add Constant Amount

Add \$400 to this amount so, \$2,116.65 + \$400, which gives \$2,516.65.
06

Calculate Salary Increment

Now accounting for Sara's years of employment over 15 years. She has been employed for 18 years, hence 3 years over 15. Calculate 1\% of the average monthly salary: \$2,516.65 * 0.01, which gives \$25.17. But as per the condition not to exceed \$100 per year, for 3 years it will be 3 * \$25.17 = \$75.51.
07

Compute Monthly Pension

Finally, add the results of Step 5 and Step 6 to find the monthly pension. This calculation is \$2,516.65 + \$75.51 = \$2,592.16.

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Key Concepts

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

Pension Calculation Formula
Understanding the pension calculation formula is critical for individuals planning their retirement or for those who are nearing the end of their employment. Pension plans can vary, but many formulas share common elements. In the case of the City of Northbeck, the formula includes several steps that work together to determine a retiree's monthly pension benefit.

It begins with calculating an average of the employee's highest earning years, shifts to a monthly perspective by dividing this average annual salary by 12, then adjusts by subtracting and adding fixed amounts, and finally, incorporates additional percentages based on years of service. The formula is systematic, guiding one through a set process to find the amount an employee would receive monthly during retirement. Each step in this calculation is designed to ensure that the pension reflects the employee's earning history and length of service.
Average Annual Salary
The average annual salary is a cornerstone in many pension calculation formulas. It represents the annual income of an employee averaged over a period, usually including the highest earning years to advantage the employee.

For instance, Sara's pension calculation starts with finding the average of her three highest annual salaries. This approach aims to provide a fair representation of an employee's earnings, as it mitigates the impact of unusually high or low earning years. To calculate this average, salaries are added together and then divided by the number of years considered, in Sara's case, three. This figure is essential because it serves as the base for subsequent adjustments which ultimately define the pension benefits.
Employment Years Pension Adjustment
Retirement benefits are not only influenced by how much you earn but also by how long you have been in service. This is where the employment years pension adjustment comes into play. It's a common feature in pension plans meant to reward long-term employees.

In the City of Northbeck's formula, for every year of employment beyond a set threshold, which is 15 years in this example, an additional percentage of the average monthly salary is tacked onto the benefit. However, there is a cap to prevent excessive rewards, keeping the system fair and sustainable. For every year Sara has worked past the 15-year mark, a 1% increase is allowed, but this bonus doesn't exceed $100 per year. This method balances rewarding experience while managing the financial stability of the pension fund.

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Most popular questions from this chapter

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