| SOA真题November2004Course8I |
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COURSE 8I: Fall 2004 -1- GO ON TO NEXT PAGE
Individual Insurance – U.S.
Morning Session
**BEGINNING OF EXAMINATION 8**
INDIVIDUAL INSURANCE – U.S.
MORNING SESSION
1. (5 points) ABC Life has a career agency distribution system. ABC’s management is
reviewing their financing plan for new agents.
(a) Describe the different types of financing plans for new agents and explain the
advantages and disadvantages of each according to LIMRA.
(b) You are given the following information:
Year Average
Annualized First
Year Premium
Agent
Termination
Rate
Subsidy Validation
Schedule
Commission
1 $60,000 50% 120% $20,000
2 $80,000 25% 80% $25,000
3 $100,000 10% 40% $30,000
4+ $120,000 0% 0% $0
%26#8226; Commissions are paid on annualized first year premium.
%26#8226; Agent termination occurs at the end of the year.
%26#8226; 6% of first year premium is priced into products to cover agent financing.
%26#8226; The interest rate is 0%.
(i) Calculate the average financing cost for a new agent as a percentage of
first year premium for each of the first three years. Show all work.
(ii) Determine the number of years it will take for ABC to recover the
financing costs on 100 new agents. Show all work.
COURSE 8I: Fall 2004 -2- GO ON TO NEXT PAGE
Individual Insurance – U.S.
Morning Session
2. (11 points) XYZ Life is evaluating a block of identical special life contingent annuities
issued January 1, 2004 by ABC Life. You are given:
%26#8226; Total required capital as a percentage of solvency reserves is 5%.
%26#8226; Assumed investment interest rate on required capital is 4%.
%26#8226; Hurdle rate is 15%.
%26#8226; Each annuity payment is $71,280.
%26#8226; Payments are made at the end of each year during the annuitant’s lifetime.
%26#8226; Deaths occur at the end of the year before the annuity payment.
%26#8226; No taxes or maintenance expenses.
Actual Projected
1/1/2004 12/31/2004 12/31/2005 12/31/2006
Policy count 100 75 50 25
Solvency reserves (‘000s) $9,864 $5,011 $1,697 $0
Premium (‘000s) $10,000 $0 $0 $0
Commission (‘000s) $400 $0 $0 $0
Benefits (‘000s) $0 $5,346 $3,564 $1,782
Investment income on
solvency reserves and
cashflows (‘000s)
$0 $838 $426 $144
(a) (3 points) Explain the process for determining the statutory valuation rate under
the Standard Valuation Law for these life contingent annuities.
(b) (4 points) Calculate the embedded value of this block at January 1, 2004. Show
all work.
(c) (3 points) You are given the following binomial distribution for mortality:
n q f(25) F(25)
100 0.25 0.0918 0.5525
Calculate the probability of solvency earnings exceeding $250,000 in 2004.
Show all work.
(d) (1 point) On January 1, 2005, XYZ Life buys the remaining block of 75
contracts.
Calculate the maximum amount of assets ABC transfers to XYZ assuming no
transaction expenses. Show all work.
COURSE 8I: Fall 2004 -3- GO ON TO NEXT PAGE
Individual Insurance – U.S.
Morning Session
3. (12 points) ABC Life is selling a deferred variable annuity product that provides for a
return of premium death benefit. ABC is considering alternative death benefit designs.
(a) (3 points) List the sectors included in an environmental analysis and evaluate the
sectors as they relate to variable annuity death benefits.
(b) (3 points) The marketing area would like to add an annual ratchet design.
(i) Compare the risk associated with the annual ratchet design to other possible
death benefit designs. Explain your answer.
(ii) Describe techniques to manage the risks associated with alternative death
benefit designs.
(c) (6 points) You are given:
Account Value on valuation date $980.00
Separate Account Value on the valuation date $980.00
Net asset charges 1%
Valuation rate 7%
Assumed year 1 drop in Account Values -14%
Assumed recovery rate 14%
Surrender charges None
Highest Anniversary Account Value $1,000.00
Average Account Value year 1 $1,009.40
Average Account Value year 2 $1,069.96
Account Value at time 1 $1,038.80
Account Value at time 2 $1,101.13
Mortality rate for year 1 0.017
Mortality rate for year 2 0.019
Survival rate from time 0 to end of year 1 0.983
Survival rate from time 0 to end of year 2 0.964
Calculate the statutory reserve for the annual ratchet death benefit at time 0, 1 and
2 using the methodology prescribed in the Valuation of Living and Death Benefit
Guarantees for Variable Annuities note. Show all work.
COURSE 8I: Fall 2004 -4- GO ON TO NEXT PAGE
Individual Insurance – U.S.
Morning Session
4. (5 points)
(a) Describe the advantages and disadvantages of:
(i) YRT reinsurance, and
(ii) Coinsurance.
(b) You are given the following information for a level term life insurance product:
Total Face Amount $100,000,000
First Year Premium $1,000,000
Policy Fee None
Premium Tax 2%
First Year Commission 50% of first year premium
Other First Year Expenses $750,000
Solvency Reserve at Issue $50,000
Assume:
%26#8226; Premium and reinsurance premium are paid annually at the beginning of
the year.
%26#8226; Unearned portion of a one-year term insurance benefit equals 50% of the
YRT reinsurance premium.
%26#8226; No federal income tax or required capital.
%26#8226; Ceded percentage equals 90%.
%26#8226; YRT reinsurance premium rate equals 0.20 per thousand of face amount.
%26#8226; Coinsurance reinsurance allowance equals 90%.
Calculate the estimated first year strain at issue for
(i) YRT reinsurance, and
(ii) Coinsurance.
Show all work.
COURSE 8I: Fall 2004 -5- GO ON TO NEXT PAGE
Individual Insurance – U.S.
Morning Session
This question pertains to the Case Study
5. (6 points) You are Saturn Life’s product management actuary for the term life insurance
portfolio. Your responsibilities include:
%26#8226; Monitoring term life new-business sales and in-force experience,
%26#8226; Advising product development, investment and marketing departments of
current developments, and
%26#8226; Reporting product profitability and capital requirements to senior
management.
(a) (1 point) Identify and describe the types of internal product management reports.
(b) (5 points) Explain how each would be used to manage Saturn’s term life
business.
COURSE 8I: Fall 2004 -6- GO ON TO NEXT PAGE
Individual Insurance – U.S.
Morning Session
6. (12 points) XYZ Life is developing a dual-life status flexible premium joint and last
survivor universal life insurance product (Survivor UL).
(a) (3 points) For pricing the Survivor UL product:
(i) Describe approaches to reflect the dual-life status including the advantages
or disadvantages of each approach.
(ii) Explain other factors to be considered in developing a mortality
assumption unique to a last survivor product.
(b) (3 points) XYZ Life’s current single-life UL products have experienced
withdrawal rates of 7% in policy year 1, grading to 5% by policy year 5.
(i) Describe considerations in setting persistency assumptions for Survivor
UL.
(ii) Propose changes to the lapse rate assumption to reflect persistency in a
volatile interest rate environment.
(c) (6 points) The following steps outline a procedure to determine minimum UL
reserves for duration t.
Revise or add information to make each step compliant with the NAIC UL Model
Regulation.
Step Procedure
1 Calculate a Guaranteed Maturity Premium (GMP) as the level premium
that provides an endowment at the latest maturity date under the contract,
calculated from the valuation date using valuation assumptions.
2 Calculate a set of Guaranteed Maturity Funds (GMF’s) as of the valuation
date using valuation basis assumptions, and assuming that gross premiums
are paid.
3 Produce a set of “guaranteed death benefits” and a “guaranteed maturity
benefit” by projecting forward from the valuation date t, using valuation
assumptions, tions, the GMFt and assuming gross premiums are paid. Calculate
the present value of these future benefits at time t ( ) PVFBt using
valuation assumptions.
4 Calculate a net level premium ( PNL ) based on the plan of insurance at
issue, using valuation assumptions, and assuming gross premiums are
paid.
5 Calculate the net level reserve at time t as NL NL
tV =PVFBt%26#8722;P
6 Calculate the CRVM expense allowance (EACRVM) for the plan of
insurance generated at issue using valuation assumptions and assuming
that PNL is paid.
7 Calculate the CRVM reserve at time t as CRVM NL CRVM
tV =tV %26#8722;EA
COURSE 8I: Fall 2004 -7- STOP
Individual Insurance – U.S.
Morning Session
7. (5 points) Your company is designing a product for the Lottery Commission. Winners
have a choice between a lump sum payment and an equivalent 25-year period certain
annuity.
(a) Describe key considerations in developing pricing assumptions for the annuity.
(b) You are considering the following product design features for the annuity:
%26#8226; Surrender provision
%26#8226; Medical bailout provision
%26#8226; Variable payout based on investment results
Describe advantages and disadvantages of including these features in the product
design.
8. (4 points)
(a) (3 points) Describe the indicators being used as preferred risk criteria for life
insurance according to the Report of the Society of Actuaries Task Force on
Preferred Underwriting.
(b) (1 point) A company with a single non-smoker class would like to introduce a
preferred class.
You are given:
%26#8226; Male age 55 aggregate mortality is 6.00 per thousand.
%26#8226; 30% of the non-smoker class is expected to qualify for the new pref[1] [2] 下一页 |
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