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Actuarial Science MLC homework help. 

For a special 3-year term life insurance policy issued to a life age 50, with a premium refund feature, you are given:Death benefit is = $100,000The premium refund feature refunds the last premium payment, without interest, at the end of the 3-year term if the insured is still alivePre-contract expenses are $155.00Commissions are 5% of each premiumThe hurdle rate is 14%0V = 01V = $4002V = $800The annual premium for this policy is $1,100q50 = .00592q51 = .00642q52 = .00697Earned interest rate in year 1 = 1%Earned interest rate in year 2 = 2%Earned interest rate in year 3 = 3%Calculate the expected profit in policy year 2

Calculate the profit vector of this policy (before consideration of survivorship)Calculate the profit signature (? = profit vector including survivorship), and the NPV, calculated using the hurdle rate.Calculate the IRR of a 3-year term life insurance policy with the following profit signature: (-155, 0, 0, 210)Provide a brief qualitative statement about this IRR (from d)) vs. the IRR for the product in a) ? c)Calculate the profit signature of the product in a) ? c) if 1V = $300 and all other values are unchangedProvide a brief qualitative statement about the IRR of this product (in f)) IRR vs. the IRR for the product in a) ? c)


1. (30 points) For a special 3-year term life insurance policy issued to a life age 50, with a

 

premium refund feature, you are given: Death benefit is = $100,000

 

The premium refund feature refunds the last premium payment, without

 

interest, at the end of the 3-year term if the insured is still alive

 

Pre-contract expenses are $155.00

 

Commissions are 5% of each premium

 

The hurdle rate is 14%

 

0V = 0

 

1V = $400

 

2V = $800

 

The annual premium for this policy is $1,100

 

q50 = .00592

 

q51 = .00642

 

q52 = .00697

 

Earned interest rate in year 1 = 1%

 

Earned interest rate in year 2 = 2%

 

Earned interest rate in year 3 = 3% a) Calculate the expected profit in policy year 2 b) Calculate the profit vector of this policy (before consideration of survivorship) c) Calculate the profit signature (? = profit vector including survivorship), and the NPV,

 

calculated using the hurdle rate. d) Calculate the IRR of a 3-year term life insurance policy with the following profit

 

signature: (-155, 0, 0, 210) e) Provide a brief qualitative statement about this IRR (from d)) vs. the IRR for the

 

product in a) ? c) f) Calculate the profit signature of the product in a) ? c) if 1V = $300 and all other values

 

are unchanged g) Provide a brief qualitative statement about the IRR of this product (in f)) IRR vs. the

 

IRR for the product in a) ? c) 2. (20 points) ABC sponsors a defined benefit pension plan. Key attributes of the pension

 

plan are: Benefits are payable as a single life annuity, paid at the beginning of each month

 

The annual benefit payable at age 65 is calculated as 2% of the final 3-year

 

average salary up to $100,000 multiplied by years of service, plus 3% of the final

 

3-year average salary over $100,000 multiplied by years of service. The monthly

 

benefit is the annual benefit divided by 12

 

i = 5%

 

A65(12) = 0.470 Connor joined ABC on 1/1/09 at exact age 40. He is planning on retiring on 1/1/34 at

 

age 65. Connor?s salary for 2014 is $80,000 and he receives annual raises of 4% each

 

January 1.

 

a) Assuming Connor works and lives until age 65, what will be his monthly benefit

 

payable as of 1/1/34? b) Calculate the Replacement Ratio at age 65, assuming Connor works until age 65 c) Calculate the expected present value of the benefit, assuming Connor works until

 

age 65 In addition to accruing a benefit in the defined benefit plan, Connor will contribute a

 

constant percentage of his annual salary to a defined contribution plan. Contributions are made at the start of each year, beginning on 1/1/2014

 

Contributions earn an investment return of 7% per year

 

The contribution balance is converted to a monthly life annuity using 5% and the

 

factor that can be derived from A65(12) = 0.470 d) Calculate the % of each year?s salary that Connor needs to contribute so that his

 

total replacement ratio is 80% 3. (20 points) For a fully discreet whole life insurance of $100,000 on a life age 35:

 

Policy Year

 

1

 

2-10

 

11+ Commission Rate

 

100%

 

10%

 

0 Per Policy Expenses

 

$100

 

$8

 

$8 Per policy expenses are incurred at the beginning of each policy year

 

i = .06

 

P = Annual Premiums

 

EPV of Premiums = 110% of the EPV of benefits, commissions, and per policy

 

expenses C = random variable for the present value at issue of commissions

 

ä35 = 15.3926

 

ä45 = 14.1121

 

10E35 = 0.54318

 

A35 = .12872

 

A45 = .201204

 

2

 

A45 = .06802

 

2

 

A35 = .03488 a) Calculate the EPV of C, in terms of P b) Calculate the EPV of per policy expenses c) Calculate P d) Calculate Var(C) 4. (10 points) For a career average pension plan with one participant currently exact age

 

55, you are given: The annual retirement benefit is 1.75% of total earnings during the participant?s

 

years of service. Retirement occurs at age 65. The retirement benefit is payable

 

monthly with the first payment at age 65.

 

Current salary after the increase at age 55 is $50,000. Future salary increases will

 

be 3% and will occur on each birthday

 

Total past earnings are $525,000 i = .04

 

ä65(12) = 12.60

 

Death is the only decrement before age 65

 

10p55 = 0.925 Calculate the actuarial present value at the participant?s current age of the annual

 

retirement benefit. 5. (10 points) You are analyzing the sensitivity of certain assumptions used in setting the

 

premium rate for a sickness policy. You are basing your analysis on a multiple state

 

model where the policyholder starts out healthy. One can go from healthy to sick or

 

dead. One can go from sick to healthy or dead. Once dead, always dead. Level premiums are paid continuously by Healthy policyholders

 

Level sickness benefits are paid continuously to Sick policyholders

 

There is no death benefit Briefly comment on the direction and impact that the following assumption changes

 

would make on the premiums (which are calculated using the equivalence principle):

 

i) Lower rate of interest and higher recovery rate from Sick state ii) A lower mortality rate for those in the Healthy state and a lower mortality rate

 

for those in the Sick state iii) A higher mortality rate for those in the Healthy state and a higher mortality rate

 

for those in the Sick state iv) A lower recovery rate from the Sick state and a lower mortality rate for those in

 

the Sick state v) A higher rate of interest and a lower mortality rate for those in the Healthy state 6. (10 points) For a special fully discreet 3-year term insurance policy on a life age 75, you

 

are given: x The death benefit during the first two years is the sum of the net premiums paid

 

without interest

 

The death benefit in the third year is $10,000

 

px 75

 

76

 

77 0.90

 

0.88

 

0.85 i = .04 Calculate the annual net premium

 


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