$4.$ Suppose that in a certain defined benefit pension plan $($a$)$ Employees work for $45$ years earning wages that increase at a real rate of $2\%,($b$)$ employees retire with a pension equal to $70\%$ of their final salary and the pension increases at the rate of inflation minus$1\%,($c$)$ The pension is received for $18$ years, and $($d$)$ the pension fund$$s income is invested in bonds which earn the inflation rate plus $1\mathrm{.}5\%.$ Estimate the percentage of an employee$$s salary that must be contributed to the pension plan if it is to remain solvent. $($Hint: Do all calculations in real rather than nominal dollars.$)$ Correct answer is $25\mathrm{.}02$