Under one plan for Social Security reform, younger workers would be able to divert up to \(\$ 1,000\) of their payroll taxes into an individual account. However, this diversion of funds would be in exchange for lower defined benefits when they retire. The reduction in defined benefits would equal the amount diverted into the individual account, compounded at a given interest rate (known as the offset rate). Using the pay-as-you-go formula, explain the impact of this plan on Social Security solvency. What would the offset rate need to be in order for this plan to have no effect on solvency? What is the relationship between the offset rate chosen and the expected money's worth ratio for the younger workers?