A life insurance company provides the following benefits (with death benefit paid at the end of policy year of death) to 60 year old policy holders:

(V) 5,000 euro if the life dies within 10 years or 5,000 euro if the life is alive in 10 years;

(W) 10,000 euro if the life dies after age 75;

(X) 15,000 euro when the life dies;

(Y) 20,000 euro if the life dies within 10 years;

(Z) 25,000 euro if the life is alive at age 70.

(i) What name is given to EACH of the benefits types in (V), (W), (X), (Y) and (Z) above?

(ii) Write out the actuarial symbol for the expected present value of EACH of the benefits in (V), (W), (X), (Y) and (Z) above.

(iii) Find the SINGLE premium for EACH of the benefits: (V), (W), (X), (Y) and (Z) above. (Assume AM92 (ultimate) mortality with an effective interest rate convertible yearly of 4 % p.a.)

b. A pension provider provides the following benefits to 65 year old pensioners:

(L) 5,000 euro p.a. for up to ten years with the the first payment now and intervals between payments of one year;

(M) 10,000 euro p.a. for up to ten years, with the first payment in a year from now and intervals between payments are one year;

(N) 15,000 euro p.a. payable for life with the the first payment now and intervals between payments of one year and

(P) 20,000 euro p.a. payable for life with the the first payment in 10 years time.

(i) What names are given to EACH of the benefits types in (L), (M), (N) and (P) above?

(ii) Write out the actuarial symbols for the expected present value of EACH of the benefits in (L), (M), (N) and (P) above.

(iii) Find the SINGLE premium for EACH of the benefits: (L), (M), (N) and (P) above. (Assume AM92 (ultimate) mortality with an effective interest rate convertible yearly of 4 % p.a.)