Imagine a bank that has raised $$900$M in funds $($total funding raised$)$ and invested these funds in a high$-$risk strategy. In this strategy, the assets $($loans$)$ generate a return equal to $7\%$ with probability $85\%,$ a return equal to $-17\%$ with probability $10\%,$ and there is a $5\%$ chance that the assets generate a return equal to $-30\%.$ For simplicity, there is only two dates in this example $($today and tomorrow$).$ The lender invests its funds today and the return on this strategy is delivered tomorrow $($cash flows only take place tomorrow$).$ Both the lender and the government discount tomorrow$$s cash flows using a $3\%$ discount rate $($independently of their risk$).$

Regulators collected the following additional information on the bank:

$89$ percent of the funds raised by the lender are deposits paying no interest.

$60$ percent of the deposits are insured by the deposit insurance fund, the remaining $40$ percent of deposits are uninsured and not protected by the deposit insurance fund.

The government wants to eliminate any subsidy created by deposit insurance to the bank and is charging the bank a deposit insurance premium today.

Calculate the $($dollar$)$ value of the deposit insurance premium today that would achieve this goal.

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