$.$ The marginal tax rate of ABC Corp is specified as below: Taxable IncomeTax rate$$0-$ $$510\%$$$5-$ $$1020\%$$$10-30\%$A firm has its taxable income as the following:Probability Pre$-$tax income $0\mathrm{.}1$ $$20$m $0\mathrm{.}9$ $$50$m$(1)$ Assume the company could purchase a zero$-$loading insurance policy. What is the premium of the insurance policy? $(2)$ Continue to assume the policy to have a zero loading. How much tax saving will ABC Corp have by purchasing the insurance policy? $(3)$ Answer $(1)$ and $(2)$ assuming the insurance policy has a $25\%$ loading.