An employee who has worked for his firm for 30 years can retire right now and receive a constant annual benefit of $45,000. He has a final pay plan that pays his average salary over his final five years x 2 percent x years of service. He has decided he will keep working five more years but only if by doing so his retirement benefits will grow at 6 percent per year. How much would his expected average salary (to the nearest dollar)have to be over the next five years to keep him working?

Question

Quizplus · Accepted Answer

To ensure the employee's retirement benefits grow at 6 percent per year over the next five years, we need to calculate the future value of his current retirement benefit at a 6 percent annual growth rate. The formula for future value is $FV = PV(1 + r)^n$, where $PV$ is the present value, $r$ is the annual interest rate, and $n$ is the number of years.Given:- $PV = $45,000$- $r = 6\% = 0.06$- $n = 5$ yearsCalculating the future value (FV):$$FV = $45,000(1 + 0.06)^5$$$$FV = $45,000(1.338225577)$$$$FV ≈ $60,220$$This is the amount the employee wants his retirement benefit to be after five more years of work.Given the retirement plan formula: Average salary over the final five years $\times 2\% \times$ years of service (35 years after 5 more years of work), we set this equal to the future value of the retirement benefit and solve for the average salary.$$Average\ salary \times 2\% \times 35 = $60,220$$$$Average\ salary \times 0.70 = $60,220$$$$Average\ salary = \frac{$60,220}{0.70}$$$$Average\ salary ≈ $86,029$$Therefore, the expected average salary over the next five years to keep the employee working would have to be approximately $86,029.

An Employee Who Has Worked for His Firm for 30