Actuarial Outpost SOA # 175
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#1
10-05-2010, 09:59 PM
 jhp8 Member Join Date: Jan 2007 Posts: 278
SOA # 175

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!
#2
10-05-2010, 11:04 PM
 Llanowan Member SOA Join Date: Aug 2010 Studying for CFA Level III College: Princeton Alumnus Favorite beer: Westvleteren 12 Posts: 468

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!?)
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#3
10-05-2010, 11:11 PM
 jhp8 Member Join Date: Jan 2007 Posts: 278

Quote:
 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!
#4
05-07-2012, 05:25 AM
 georgestouma Member CAS SOA Join Date: Mar 2012 Studying for C College: Postgraduate Posts: 457

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) ?
#5
05-07-2012, 10:07 AM
 nin01001 Member Join Date: Jul 2011 Posts: 45

The expected fund is being set up with equivalence in mind, so they are collecting just what they need to end with 0.
#6
05-07-2012, 04:34 PM
 georgestouma Member CAS SOA Join Date: Mar 2012 Studying for C College: Postgraduate Posts: 457

Quote:
 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

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