A financial investor is looking to purchase a new portfolio. Hedge Fund A $($HFA$)$ o$3$ers a portfolio that is

worth an expected $35$mil. HFA has analysts who can build a model to boost this portfolio. The boost

would add an amount that has a Normal Distribution with mean $3$mil and standard deviation $0\mathrm{.}5$mil.

HFA wishes to sell his financial services at a fee that guarantees his expected profit will be $5\%$ of the

total value of the portfolio.

A$)$ Calculate the fee of HFA$$s financial services.

$[5$ marks$]$