A bank has $$25$ million in assets, $$20$ million in liabilities, and $$5$ million in shareholders' equity.

The bank is looking at $3-$year maturity zero$-$coupon bonds and $5\%$ yield perpetuities to immunize its

interest rate risk. If the duration of its liabilities is $9$ years and the bank wants to immunize its net

worth against interest rate risk and thus set the duration of equity equal to zero, it should invest

$\_\_\_\_\_\_\_\_\_\_$ of the portfolio value in the zero$-$coupon bonds.