You are given: a. A death benefit of $450 is paid at the end of the...

You are given:
a. A death benefit of $450 is paid at the end of the year in which the policy
holder dies
b. The annual interest rate is 5%
c. Mortality is given by q 35+t = 0.02+0.01t
Calculate the value of a 3 year term life insurance for a 35 year old.

Expert Solution

Given, the death benefit is $ 450 which is paid at the end of the year in which the policy holder dies.

The current age of the policy holder is 35 years.

The annual interest rate is i = 5%

the discount rate is v = 1 / (1 + i) = 1.05-1

The mortality rate is q35 + t = 0.02 + 0.01 * t

The value of a 3 year term life insurance for a 35 year old is

PV = (450 * q35 * v) + (450 * p35 * q36 * v2) + (450 * 2p35 * q37 * v3)

= (450 * q35 + 0 * v) + (450 * (1 - q35 + 0) * q35 + 1 * v2) + (450 * (1 - q35 + 0) * (1 - q35 + 1) * q35 + 2 * v3)

= (450 * 0.02 * 1.05-1 ) + (450 * (1 - 0.02) * (0.02 + 0.01 * 1) * 1.05-2) + (450 * (1 - 0.02) * (1 - (0.02 + 0.01 * 1)) * (0.02 + 0.01 * 2) * 1.05-3)

= 8.5714 + 12 + 14.7810

PV = 35.3524

So, the required value is $ 35.35.

orchestra answered 2 years ago

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