Red Rock would like to purchase an office building at the price of $$36\mathrm{.}8$ million. The building has a cap rate of $9\%.$

To finance the purchase, Red Rock approaches Sitea bank for a mortgage.

Sitea bank offers a mortgage with a $5-$year balloon and $30-$year term at the interest rate of $10\%$ p$.$a$.,$ compounded monthly.

Sitea requires LTV to be less than $65\%$ and DSCR to be at least $1\mathrm{.}5.$

Red Rock needs to contribute at least $ $\_\_\_$ million of equity for the purchase.