A life insurance company provides the following benefits (with death benefit paid at the end of policy year of death) to 55 year old policy holders:

(V) 15,000 euro if the life dies within 20 years or 15,000 euro if the life is alive in 20 years;

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

(X) 25,000 euro when the life dies;

(Y) 30,000 euro if the life is alive at age 75;

(Z) 35,000 euro if the life dies after age 80.

(a) (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 net 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.)