Let Y denote the present value of a ten-year deferred 30-year temporary life annuity- 100, immediate on (30). If i = 0 and mortality is uniformly distributed with w = calculate the probability that the sum of the payments will exceed E (Y).

Let Y denote the present value of a ten-year deferred 30-year temporary life annuity- immediate on (30). If i = 0 and mortality is uniformly distributed with w = = 100, calculate the probability that the sum of the payments will exceed E(Y).

A piece of equipment is being insured against early failure. The time from purchase until failure of the equipment is exponentially distributed with mean 10 years. The insurance will pay an amount x if the equipment fails during the first year, and it will pay 0.5x if failure occurs during the second or third year. If failure occurs after the first three years, no payment will be made. Calculate x such that the expected payment made under this insurance is 1000.

A life insurance company issues a whole life annuity immediate with annual payments. The annuity is issued to (65). The annuity pays 50,000 at the end of each year for the life of the annuitant with the first payment being made at age 66. You are given: A single premium is paid to purchase this annuity. Mortality follows the Illustrative Life Table with i = 0.06. %3D Assume that the single net premium, P, is 1 of the expected present value at issue of benefits. Calculate the probability that this policy will generate a profit using P.

Find the expected value of the yearly rate of return of an investment that, for an initial cost of 100, is equally likely to yield either 120 or 100 after 2 years.

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is 200,000, what is the expected population after 5 years? tion of a certain city in the southwest will increase by 8% during each of the next 5 years. If the current population POPULATION GROWTH It has been projected that the popula- during each of the next 5 years. If the current population is 200,000, what is the expected population after 5

A retiree is offered the choice of two continuous annuities:− A life annuity, paying 30,000 per year.− A life annuity with a 5-year certain period, i.e., an annuity paying benefits for life,but with a minimum pay-out period of 5 years.The benefit amount for the second annuity is chosen so that the expected present valueof the two annuities is the same. Given ? = 0.02 and ? = 0.07, determine the annualbenefit amount of the second annuity, ??

The annuity will run out of funds after approximately 13 years 10 months. (b) Show that a continuous annuity with withdrawal rate N = $5000/year and interest rate r = 8%, funded by an initial deposit of P0 = $75,000, never runs out of money.

Consider a special fully discrete 20 year endowment insurance on (30). The death benefit, payable at the end of the year of death if death occurs within 20 years, is 250,000, while the endowment benefit which is payable at time 20 is 500,000. Premiums are level and payable at the beginning of each year for 20 years. Using the Standard Ultimate Life Table ( S.U.L.T) with i = 5% determine each of the following: (a.) the premium 7. (b.) 10 V, the reserve at time 10.