$In$ the last quiz, $we$ found that Alexander needed $$5,931,432\mathrm{.}03on$ hand $to$ begin retirement.

Alexander $is22,$ expects $to$ retire $at$ age $68,$ and end retirement $at$ age $100.$ The anticipated annual investment return $is12\%$ and the anticipated annual inflation rate $is5\%,$ making the real annual rate $of$ return $an$ anticipated $6\mathrm{.}6667\%.$

Using the capital preservation approach, how much more money will Alexander need $to$ begin retirement?