A defined benefit plan has $100$ employees, most of whom are over age $40.$

The pension fund manager has collected the following data:

Risk$-$free rate $2\mathrm{.}50\%$

S&P $500$ return $(5-$year average$)9\mathrm{.}87\%$

Expected inflation rate $2\mathrm{.}10\%$

Discount rate used to compute pension obligation $5\mathrm{.}95\%$

Yield to maturity on the company $20-$year bonds $6\mathrm{.}28\%$