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Thomas H
May 5th 2007, 04:11 PM
For a fully discrete whole life insurance policy of 1000:

1) The benefit premium is 30.
2) The expense premium is 7.
3) 1st year expenses - percent of premium = 95%, per 1000 = 10
4) renewal expenses - percent of premium = 10%, per 1000 = 2
5) Expenses are payable at the beginning of the year
6) 3_V^e = -21
7) 1_q_{x+3} = 0.02
8) i = 0.05

Determine 4_V^e

Here is the solution:

4_V^e = (3_V^e +P^e - cG - e) (1+i) / (1 - 1_q_{x+3})

4_V^e = (-21 + 7 - 0.1(30 + 7) - 2)(1.05) / 0.98

Isn't the expense premium G?

In lesson 45 the expense reserve formula is stated as:

t_V^e = [{t-1}_V^e + e - Gc_{t-1} - e_{t-1} ](1+i) / 1_p_{x+t-1}

Where is this P^e coming from in the solution?

Abraham Weishaus
May 6th 2007, 08:36 AM
With 2 options in the textbooks, you should concentrate on the concepts rather than the notation.

G is the gross premium, which is the contract premium, the amount actually charged. P^e and e (they're both the same) are the expense premium, the level amount needed to pay expenses. When rolling forward the expense reserve, this must be added in, the same way the benefit premium is added in when rolling forward the benefit reserve.