Designing a 401(k): A Case Study

Over the past decade or so, many private and publicly held companies have moved away from providing employees with company-funded pensions upon retirement to a retirement system that requires both employee and company contributions to fund an individual’s retirement. These so-called 401(k) retirement plans usually require the employee to choose among different investment vehicles, including mutual funds, in order to allocate their retirement savings. This study presents the results of an analysis of the allocation of a lump-sum rollover of money into a typical 401(k) plan, subject to certain restrictions. The mathematics required to complete this analysis includes those topics that are typically covered in an undergraduate course in linear algebra. All of the following material was used in a sophomore-level engineering mathematics course taught at Rowan University.