Question

Suppose that a lifetime is either 1 year or 2 years uniformly. Our company has a 4000 benefit life insurance with this life. Assume a constant force of interest of 0.01

a) If the life was in fact 1 year, then what is the present value of the benefits?

b) What are the chances that the present value of the benefits is the above?

c) What is the other possible value for the present value of the benefits of this insurance contract?

d) What is the variance of the present value of the benefits of this insurance contract?

Answer 1

a)If the life was in fact 1 year, then what is the present value of the benefits = 4000/(1+r)

here r=0.01

=4000/(1.01)

=$3960.39

b)chances that the present value of the benefits is the above =0.5 ( As even)

c)Other possible value for the present value of the benefits of this insurance contract = present value for 2 years

=4000/(1.01)^2

=$3921.18

d)mean of the present value of the benefits of this insurance contract =(3960.39+ 3921.18)/2

=$3940.78