精算师考试试题(10) 

Faculty of ActuariesInstitute of Actuaries

EXAMINATIONS

6 September 2001 (pm)Subject 201— Communications

Time allowed: 1? hours

INSTRUCTIONS TO THE CANDIDATE

Write your surname in full, the initials of your other names and your Candidate’sNumber on the front of the answer booklet.

AT THE END OF THE EXAMINATION

Hand in BOTH your answer booklet and this question paper.

In addition to this paper you should have availableActuarial Tables and an electronic calculator.

201—S2001

? Faculty of Actuaries? Institute of Actuaries

Your employer, an insurance company, is developing a new lump sum investmentproduct with a fixed 5 year term. The amount paid out will be based on the value of awidely used and publicly quoted index. Two options are under consideration.

Option A

After 5 years, this pays out 100% of the amount invested, plus a further 8% of theamount invested for every year that the index at the anniversary exceeds theindex at the preceding anniversary by at least 4%.Option B

After 5 years, this pays out the amount invested increased by the ratio of theindex at the maturity date to the index at the start date.

The customer always receives at least the return of their original investment.

A senior manager from your company has written to you. He has calculated that for a￡10,000 investment, using your standard company assumption of 5% index growth eachyear, the amount payable on option A would be ￡14,000. He has not calculated the

amount payable for option B, but has said that it looks to be considerably lower than foroption A. He has asked you whether this is correct, and whether he has correctlyunderstood the way that the maturity payments are calculated.

Draft a memo in 500 to 600 words comparing the amounts payable after 5 years foroptions A and B.Notes:

? You should not question the reasonableness of the 5% standard company assumption

on the rate of index growth over the five year investment period. However, youshould make use of the fact that this is an average over the five years, and the rateof growth is likely to fluctuate over time.? An actuarial student has calculated the following figures rounded to the nearer ￡50:

Number of yearswhere the indexgrowth exceeds 4%

12345

Example profile ofannual growth, basedon average of 5%, 2%, 2%, 2%, 2%8%, 8%, 3%, 3%, 3%7%, 6%, 6%, 3%, 3%6%, 6%, 5%, 5%, 3%5%, 5%, 5%, 5%, 5%

Maturity amountfor Option A

￡10,800￡11,600￡12,400￡13,200￡14,000

Maturity amountfor Option B

￡12,750￡12,750￡12,750￡12,750￡12,750

? You should not consider the surrender values within the 5 year investment period.? You should not consider the choice of index or technical details of how it is

calculated.

? You are not required to discuss how the monies received by the insurance company

should be invested.

201 S2001—2