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Peterson Products calculates its pension benefits as follows: Years of service × 1.98% multiplier × Average of last two annual salaries What is Mary’s monthly pension benefit if she worked for Peterson for 28 years and her last two annual salaries were \(\$ 78,000\) and \(\$ 80,000\) ?

Short Answer

Expert verified
The monthly pension benefit of Mary who worked for Peterson for 28 years and had her last two annual salaries as \(78,000\) and \(80,000\) can be calculated using Peterson's pension calculation formula. The result is obtained after finding the average of her last two salaries, multiplying it by her years of service and the benefit multiplier, and then dividing it by the number of months in a year to get the monthly pension.

Step by step solution

01

Calculate Average Salary

First, find the average of Mary's last two salaries which are \(\$ 78,000\) and \(\$ 80,000\). The formula for average is (Sum of items) divided by (Number of items), here number of items is 2. Average salary = (\(\$ 78,000 + \$ 80,000)/2
02

Apply Pension Benefit Formula

Next, apply the formula for calculating pension benefits, which is (years of service x multiplier x average salary). Here, the years of service are 28, the multiplier is 1.98%, and the average salary we've calculated in Step 1.
03

Monthly Pension Benefit Calculation

Finally, to calculate the monthly pension benefit, divide the annual benefit obtained in Step 2 by the number of months in a year, which is 12. Monthly pension = Annual pension / 12

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Key Concepts

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

Average Salary Calculation
Understanding how to calculate the average salary is fundamental to pension calculations. To find Mary’s average salary, we take her last two annual salaries and compute their average. This involves summing the two salary figures and then dividing by the number of salaries.
For example, if Mary's last two annual salaries are \( \\(78,000 \) and \( \\)80,000 \), the calculation is as follows:
\[ \text{Average Salary} = \frac{\\(78,000 + \\)80,000}{2} = \\(79,000 \]
Thus, for Mary, the average annual salary upon which her pension benefit will be based is \( \\)79,000 \). This average salary ensures that the pension benefit is reflective of her most recent earnings, ensuring fairness and accuracy.
Annual Benefit Formula
The annual benefit formula is a key component in determining pension benefits. This calculation helps us understand how much Mary will earn annually from her pension based on her service to the company. The general formula involves multiplying the years of service by a given percentage multiplier and then multiplying that result by the average salary computed earlier.
In Mary’s case, the calculation looks like this:
* **Years of Service:** 28
* **Multiplier:** 1.98% or 0.0198
* **Average Salary:** \( \\(79,000 \)
The formula is expressed as:
\[ \text{Annual Benefit} = \text{Years of Service} \times \text{Multiplier} \times \text{Average Salary} \]
Plugging in Mary’s values, we get:
\[ 28 \times 0.0198 \times \\)79,000 = \$43,834.40 \]
This is the annual benefit amount from which Mary's pension earnings are based.
Monthly Pension Benefit
Once the annual pension benefit amount has been calculated, converting it to a monthly value is straightforward. This step is crucial because pensions are typically distributed on a monthly basis.
To determine the monthly pension benefit from the annual figure, divide the annual pension by the number of months in a year – 12.
For Mary, the calculation is:
\[ \text{Monthly Pension} = \frac{\text{Annual Pension}}{12} = \frac{\\(43,834.40}{12} = \\)3,652.87 \]
This means Mary will receive a monthly pension benefit of approximately \( \$3,652.87 \). Converting the annual figure to a monthly figure helps beneficiaries like Mary plan their finances better during retirement.
Years of Service Impact
The number of years a person has worked significantly impacts their pension benefit. In pension calculations, years of service reflects loyalty and contributions to the company over time, directly affecting the size of the pension.
The formula uses years of service as a multiplier component, which means the more years worked, the larger the benefit because this factors into the amount paid out.
For example, in Mary's case with 28 years of service, her years not only make her a long-standing employee but also substantially increase her annual benefit.
* **More years generally mean**:
  • Larger annual benefit.
  • Increased monthly retirement income.
This encourages employee retention, as long-term service can result in a more secure financial payout upon retirement. Thus, understanding the impact of years of service is critical in planning for the future.

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Most popular questions from this chapter

The Morning Sun offers employees 1.65\(\%\) of the average of their last three years of annual compensation for each year of service. Ramon began working for the Morning Sun in 1988 . He retired in 2010 . In 2008 , he made \(\$ 76,000\) per year. Thereafter, he received a 3\(\%\) salary increase each year until he retired. How much was his annual retirement benefit?

Mark is an accountant who has been contributing to his retirement account for the last 15 years with pretax dollars. The account com- pounds interest semi- annually at a rate of 5\%. He contributes \(X\) dollars after each 6 -month period, and this has not changed over the life of the account. a. How much will he have in the account after 20 years of saving? Round numbers to the nearest hundredth. b. After 20 years of contributions, he needed to withdraw 20\(\%\) of the money in his account to pay for his children's education. Write an expression for the withdrawal amount. c. Mark pays \(T\) percent of his income in taxes. Write an algebraic expression for the combined total of his tax and the 10\(\%\) early withdrawal penalty.

Laura has been contributing to a retirement account that pays 4\(\%\) interest with pretax dollars. This account compounds interest monthly. She has put \(\$ 500\) per month into the account. At the end of 10 years, she needed to pay some medical bills and had to withdraw 15\(\%\) of the money that was in the account. a. Rounded to the nearest dollar, how much did she withdraw? b. Laura pays 23\(\%\) of her income in taxes. What was her tax on the amount of the withdrawal (rounded to the nearest dollar)? c. She had to pay a 10\(\%\) early withdrawal penalty. How much was she required to pay, rounded to the nearest dollar?

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.

At the age of \(30,\) Jasmine started a retirement account with \(\$ 50,000\) which compounded interest semi-annually with an APR of 4\(\%\) . She made no further deposits. After 25 years, she decided to withdraw 50\(\%\) of what had accumulated in the account so that she could contribute towards her grandchild's college education. She had to pay a 10\(\%\) penalty on the early withdrawal. What was her penalty?

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