The Certainty Company $($CC$)$ operates in a world of certainty. It has just hired Mr$.$ Jones, age $27,$ who will retire at age $65,$ draw retirement benefits for $6$ years, and die at age $71.$ Mr$.$ Jones$$ salary is $$21,000$ per year, but wages are expected to increase at the $4\%$ annual rate of inflation. CC has a defined benefit plan in which workers receive $1\%$ of the final year$$s wage for each year employed. The retirement benefit, once started, does not have a cost$-$of$-$living adjustment. CC earns $10\%$ annually on its pension fund assets and uses a $9\%$ rate to discount its expected future benefit payments. Assume that pension contribution and benefit cash flows occur at year$-$end. Do not round intermediate calculations. Round your answers to the nearest dollar.

$*$ How much will Mr$.$ Jones receive in annual retirement benefits?

$*$ What is CC$$s required annual contribution to fully fund Mr$.$ Jones$$ retirement benefits?

$*$ Assume now that CC hires Mr$.$ Smith at the same $$21,000$ salary as Mr$.$ Jones. However, Mr$.$ Smith is $33$ years old. Repeat the analysis in parts a and b under the same assumptions used for Mr$.$ Jones. What is CC$$s required annual contribution to fully fund Mr$.$ Smith$$s retirement benefits?

$*$ What do the results imply about the costs of hiring older versus younger workers?$$From a pension funding standpoint alone, CC would favor a$($an$)($younger$/$older$)$worker as the$($younger$/$older$)$worker requires higher annual pension fund contributions.

$*$ Now assume that CC hires Ms$.$ Brown, age $27,$ at the same time that it hires Mr$.$ Smith. Ms$.$ Brown is expected to retire at age $65$ and to live to age $78.$ What is CC$$s annual pension cost for Ms$.$ Brown?

$*$ If Mr$.$ Jones and Ms$.$ Brown are doing the same work, are they truly doing it for the same pay?$$The company is actually "paying" Ms$.$ Brown$($more$/$less$)$ than they are paying Mr$.$ Jones.