Paul was injured in an accident. In addition to considerable discomfort, the best estimate is that his medical expenses in $2009$ will be $$100,000.$ In the future, those expenses will increase at $10\%$ per year. Paul had been earning $$50,000$ per year, but will only earn $80\%$ of that in the future. Labor economists expect those in Paul$$s occupation to experience a $3\%$ annual increase in earnings. Assume Paul has a $10-$year work life and a $20-$year expected natural life remaining. Also assume that the appropriate discount rate is $5\mathrm{.}0\%\mathrm{.}1.$ How much should Paul be awarded? $($Ignore tax considerations.$)$

$2.$What is the present value of $$500,000$ to be received in $20$ years if the discount rate is $6\mathrm{.}0$ percent?

$3.$What is the present value of $$80,000$ per year for $10$ years at a discount rate of $9\mathrm{.}0$ percent?