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 5 years times 2% times 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% per year. How much would his expected average salary (to the nearest dollar) have to be over the next 5 years to keep him working?

Question

Quizplus · Accepted Answer

First, we need to calculate how much the employee's retirement benefits would be worth in 5 years if they grew at 6% per year. Using the formula for future value of a lump sum:

FV = PV x (1 + r)^n

where FV is the future value, PV is the present value, r is the interest rate per period, and n is the number of periods.

In this case, the present value (PV) is $45,000, the interest rate (r) is 6%, and the number of periods (n) is 5. So:

FV = $45,000 x (1 + 0.06)^5 
FV = $63,624

So if the employee keeps working for 5 more years and his retirement benefits grow at 6% per year, he would receive an annual benefit of $63,624.

Now we need to use the formula for the final pay plan to find out what his average salary over the next 5 years would need to be in order to get this benefit. The formula is:

Benefit = Average salary x 2% x years of service

We know that the years of service will be 35 (30 years worked so far, plus 5 more to come). We also know the benefit ($63,624) and the 2% multiplier. So we can rearrange the formula to solve for average salary:

Average salary = Benefit / (2% x years of service)

Plugging in the numbers:

Average salary = $63,624 / (2% x 35) 
Average salary = $86,028.57

To the nearest dollar, the expected average salary over the next 5 years would need to be $86,029 to keep the employee working. Therefore, the best choice is B.

An Employee Who Has Worked for His Firm for 30