In calculating insurance premiums, the actuarially fair insurance premium is the premium

that results in a zero NPV for both the insured and the insurer. As such, the present value

of the expected loss is the actuarially fair insurance premium. Suppose your company

wants to insure a building worth $$410$ million. The probability of loss is $1\mathrm{.}37$ percent in

one year, and the relevant discount rate is $4\mathrm{.}4$ percent.

a$.$ What is the actuarially fair insurance premium? $($Do not round intermediate

calculations and enter your answer in dollars, not millions of dollars, rounded to

the nearest whole number, e$.$g$.,1,234,567.)$

b$.$ Suppose that you can make modifications to the building that will reduce the

probability of a loss to $\mathrm{.}95$ percent. How much would you be willing to pay for these

modifications? $($Do not round intermediate calculations and enter your answer in

dollars, not millions of dollars, rounded to the nearest whole number, e$.$g$.,$

$1,234,567.)$

a$.$ Insurance premium

b$.$ Maximum cost