Raj expects his future earnings to be worth Rs 100. If there is some unfortunate event, his expected future earnings will be Rs 25. The probability of an unfortunate event to occur is 23, while that of things remaining fortunate is 13. Suppose his utility function is given by U(Y) = 12 , where Y represents the amount of money. Now suppose an insurance company offers to fully insure Raj against the loss of earnings caused during an unfortunate event at an actuarially fair premium.

(i) Will Raj accept the insurance? Explain.

(ii) What would be the rate of actuarially fair premium charged in this case?

(iii) What would be the maximum amount that Raj would pay for the insurance?