Question

Suppose that a lifetime is either 1 year or 2 years uniformly. A company has a...

Suppose that a lifetime is either 1 year or 2 years uniformly. A company has a 4000 benefit life insurance with this life. Assume a constant force of interest of .01

Prove that the variance is equal to 388.181448248629

Math   Statistics-And-Probability   
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Answer #1

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

r=0.01

PV(1) =4000/(1.01)

=$3960.39

The present value of the benefits of this insurance contract for 2 years = 4000/(1+r)2

PV(2) =4000/(1.01)2

=$3921.18

Now ,mean of the present value of the benefits of this insurance contract = [PV(1) +PV(2)]/2

= (3960.39 + 3921.18)/2

=$3940.78

Variance =

=

=

= 768.7121

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