SOA # 175

[jhp8]

Question:

A group of 1000 lives each age 30 sets up a fund to pay 1000 at the end of the first year for each member who dies in the first year, and 500 at the end of the second year for each member who dies in the second year. Each member pays into the fund an amount equal to the single benefit premium for a special 2-year term insurance, with:

(i) Benefits:
k bk +1
0 1000
1 500

(ii) Mortality follows the Illustrative Life Table.

(iii) i = 0.06

The actual experience of the fund is as follows:

k Interest Rate Deaths
0 0.070 1
1 0.069 1

Calculate the difference, at the end of the second year, between the expected size of the fund as projected at time 0 and the actual fund.
*************************************************

I calculate the initial fund to be 2158.85 like the answer key says. However, I don't understand the next step of the solution:

Let Fn denote the size of Fund 1 at the end of year n.
F1=2158.75*(1.07) −1000 = 1309.86
F2=1309.86*(1.065) −500 = 895.00

Why do they use a interest rate of 6.5%? I would think a 6.9% interest rate should be used.

Thanks!

[Llanowan]

It should be 6.9, it's just an error. If you use 6.9, you'll get:

2158.75(1.07)-1000 = 1309.86
1309.86(1.069) - 500 = 900.24, which still gives you your 900 (C).


If I had my guess, they wrote the question as 6.5% (or perhaps it appeared that way on an exam) and they intended you to round to 900, but when they added it to the sample questions, they backed into the .069 to get an answer closer to 900. (Or maybe it was just an error, who knows!?)

[jhp8]

Originally Posted by Llanowan

It should be 6.9, it's just an error. If you use 6.9, you'll get:

2158.75(1.07)-1000 = 1309.86
1309.86(1.069) - 500 = 900.24, which still gives you your 900 (C).


If I had my guess, they wrote the question as 6.5% (or perhaps it appeared that way on an exam) and they intended you to round to 900, but when they added it to the sample questions, they backed into the .069 to get an answer closer to 900. (Or maybe it was just an error, who knows!?)

Thanks. For some reason I thought 895 was a answer choice (Which it is not) and thought I was getting the sucker answer. I wish they would fix their solution, I wasted to much time on that!

[georgestouma]

why the expected fund at end of year 2 is 0 ? So they are using the reserve at time 2 witch need the mortality .. Why in the solution in F1 they didnt divide by (1-0.001) ?

[nin01001]

The expected fund is being set up with equivalence in mind, so they are collecting just what they need to end with 0.

[georgestouma]

Originally Posted by nin01001

The expected fund is being set up with equivalence in mind, so they are collecting just what they need to end with 0.

Thanks. But why they are not using the same way in expecting in the fund , they didnt divide it by Px =1-0.001 =one per 1000 die