A county government has a pension plan for its employees in which a graded vesting formula is applied. Full vesting in a pension occurs when an employee completes 20 years of services. In a fully vested pension, a retiree from this county government has her pension calculated by multiplying her number of years of service, her average salary from her last three years of employment, and a multiplier of 2.2%. The pension is reduced if full vesting has not yet occurred. For instance, as shown in the table below, an employee who retires after completing 15 years of service receives only 60% of the multiplier that would apply to a fully vested retiree.
|Years of Employment||Vesting Percentage|
|5 or less||0%|
|6, 7 or 8||20%|
|9, 10 or 11||40%|
|12 or 13||50%|
|14 or 15||60%|
|16 or 17||70%|
|18 or 19||85%|
|20 or more||100%|
Decide whether the following statements are true or false about this scenario.
An employee who worked for 15 years with an average salary of $57,800 for his last three years of service would receive a pension equal to less than one-quarter of his average salary.
An employee who worked for 18 years with an average salary of $61,200 for her last three years of service would receive a pension that is 15% greater than an employee with the same average salary who worked only 17 years.
An employee can receive a pension equal to half of his average salary only if fully vested.