A pension plan is a retirement plan that requires an employer to make contributions into a pool of funds set

aside for a worker$$s future benefit. The pool of funds is invested on the employee$$s behalf, and the earnings

on the investments generate income to the worker upon retirement. According to a recent article on pension

liability from the Economist, The Centre for Retirement Research $($CRR$)$ at Boston College has looked at

around $4,000$ American state and local$-$government pension plans. When using the accounting standards

permitted $($i$.$e$.,$ using assumed rate of return on the pension assets, typically $7$ to $8\%),$ the plans were on

average $72\%$ funded at the end of $2015.$ On a more conservative $4\%$ rate of return, this drops to $45\%.$ On the

former basis, the collective deficit is $$1\mathrm{.}2$ trillion; on the latter $$4\mathrm{.}1$ trillion. Which discount rate is a more

appropriate one to use? Justify your answer.

Note: Government pension plans are defined benefit pension plan in which an employer promises a specified

pension payment, lump$-$sum, or combination of both on retirement that is determined by formula. The

formula is known in advance