The Cerlainty Company $($CC$)$ operates in a world of certainty. It has just hired Mr$.$ Jones, age $32,$ who will retire at age $65,$ draw retirement benefits for $20$ years, and die at age $85.$ Mr$.$ Jones' salary is $$20,000$ per year, but wages are expected to increase at the $6\%$ 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 $7\%$ annually on its pension fund assets and uses a $7\%$ 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.

a$.$ How much will Mr$.$ Jones receive in annual retirement benefits? $5$

b$.$ What

is$.$cC$\text{'}$s required annual contribution to fully fund Mr$.$ Jones' retirement benefits?

$

c$.$ Assume now that CC hires Mr$.$ Smith at the same $$20,000$ salary as Mr$.$ Jones. However, Mr$.$ Smith is $44$ years old. Repeat the analysis in parts a and b under the same assumptions used for Mr$.$ Jones. What is CC$\text{'}$s required annual contribution to fully fund Mr$.$ Smith's retirement benefits? s

What do the results imply about the costs of hiring older versus younger workers?

From a pension funding standpoint alone, $CC$ would favor $a(an)$ worker as the $$ worker requires higher annual pension fund contributions.

d$.$ Now assume that $CC$ hires Ms$.$ Brown, age $32,$ at the same time that it hires Mr$.$ Smith. Ms$.$ Brown is expected to retire at age $65$ and to live to age $91.$ What is CC$\text{'}$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 $$ than they are paying Mr$.$ Jones.