Course 3 - Insurance problem

[Agtuary]

Twenty years ago, a fully discrete whole life policy was issued to John, then aged 30. The future premium payments are currently sufficient to fund one-third of the death benefit. The equivalence principle is assumed.

If P50 = 0.06 and a(due)30 = 10, find A50

Ans. 3/7

How do I do this problem?

[Nelle]

Are you sure this is the right info?

[Agtuary]

The information is correct. To clarify P50 is the premium, not the probability of survival.

[Agtuary]

Here is the solution (at least it gets me close enough i.e, 30/71):

P50 = 1/3 A30 => 0.06 = 1/3[1-d*a(due)30] => d = .082

P50 = A50/a(due)50 = [d*A50]/[1-A50] => 0.06 = 0.082A50/[1-A50]

solving for A50 gives 0.4225352 and 3/7 = 0.42857

[Nelle]

I got d=.08 which gives 3/7 exactly, but it will take me a minute to figure out how to type it in.

[Nelle]

1) A30=10P30

2) 1/3*A50=P30*a(due)50
A50=3P30*a(due)50


3) A50=.06*a(due)50

substitute 3 into 2 and cancel ==> P30=.02

=> A30=.2 => d=.08

[Agtuary]

I asked this question because I did not understand the sentence "The future premium payments are currently sufficient to fund one-third of the death benefit."

It appears the interpretation I chose was incorrect. The way I went about the problem was also poor, I just lucked into a close answer. Let's hope this happens a lot on the exam! Cause right now I think I will be discussing these items with everyone in October.

[Nelle]

It is a little ambiguous...

[Exam Slave]

I'm leaning toward Nellie on this one.
"P50 = 1/3 A30 " is not necessarily true.
Since this statement causes your 'd' to be slightly incorrect, your answer turns out slightly incorrect.

[Agtuary]

I agree. At a minimum I should have said P50*a(due)50 = 1/3 A30. That is why I said I approached the problem poorly. I just lucked into an answer.

[8 iron]

The paid-up reserve formula states that nVx = (1 - Px/Pn+x)Ax+n. The ratio of the premiums (Pn/Pn+x) identifies the portion of future premiums funded by future benefits.

Therefore, for this problem, P30/P50 = 1/3. Solving for P30 = 0.02. Thus, 0.02 = (1-da(due))/a(due).
0.02 = (1 - 10d)/10
d = 0.08.

Now solve for A50 using the P50 premium that was given:

0.06 = A50 / [(1 - A50) / 0.08].

A50 = 3/7.

Hope this helps.