For a fully discrete 3-year term life insurance policy on (60), you are given:
* (i) The death benefit is 100,000.
* (ii) Mortality follows the Illustrative Life Table.
* (iii) The rate of interest is based on the yield curve at (t = 0).
You are also given the following information about zero coupon bonds based on the yield curve at (t = 0):
| Years to Maturity | 1 | 2 | 3 |
| Price of 100 Bond | 97.00 | 92.00 |
Calculate the benefit premium.
Solution
From the Illustrative Life Table, we have (q_{60} = 0.01376), (q_{61} = 0.01501), and (q_{62} = 0.01638).
For this 3-year term insurance, the expected present value of future benefits is
begin{eqnarray*}
100000 A_{60:overline{3|}}^{~1} &=& 1000000left(v_1 q_{60} + v_2 ~_{1|} q_{60} + v_3 ~_{2|} q_{60} right) \
&=& 1000000left((0.97) q_{60} + (0.92) p_{60} q_{61} + (0.87) p_{60}p_{61} q_{62} right) \
&=& 1000000left((0.97)(0.01376) + (0.92)(0.98264)(0.01501) right.\
& ~& ~~~~~~~ left.+ (0.87)(0.98264)(0.98499)(0.01638) right) = 4,070.969.
end{eqnarray*}
The expected present value of an annuity is
begin{eqnarray*}
ddot{a}_{60:overline{3|}} &=& 1 + v_1 ~ p_{60} + v_2 ~_2 p_{60} \
&=& 1 + (0.97)(0.98264) + (0.92)(0.98264)(0.98499)= 2.850374.
end{eqnarray*}
Thus, the annual benefit premium is $ 4,070.969/2.850374= 1,431.74