STOR 471Exam 2
November 11, 2013
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(1) If i = 0.06, calculate the actuarial present value of each of the following payments:
(a) $1000 payable at th
Homework Assignment 3: (1) A bank offers the following certificates of deposit: Term in years 1 2 3 4 Nominal annual interest rate compounded semi-annually 5% 6% 7% 8%
The certificates mature at the end of the term. The bank does not permit early withdraw
Homework Assignment 2: (1) Complete the following table: Accumulated value of 100 at end of 2 years i(4) = 0.06 d(12) = 0.06 (Ans: 112.65 112.78 55.13 54.80) Present value of 100 payable at end of 10 years
(2) Determine the nominal rate of interest compou
Homework Assignment 1: (1) This problem refers to Professor Robert Shiller's lecture on insurance from his 2008 Financial Markets course at Yale. You can find the lecture at
http:/www.youtube.com/playlist?list=PL8F7E2591EE283A2E&feature=plcp
Select Lectur
Homework Assignment 24: (1) You are given that mortality follows De Moivre's law with = 100 and i = 0.05. Calculate 10Vcfw_4(40). (Ans 0.075) (2) A fully discrete whole life policy with quarterly premiums is issued to a life age x on August 1. The benefit
Homework Assignment 23: (1) Exercise 7.8 on page 226.
(2)
Given that mortality follows the Illustrative Life Table and i = 0.06, use the prospective formula to calculate 10V30. (Ans 0.0655594)
(3) For a fully discrete whole life insurance of 1000 issued t
Homework Assignment 22:
(1) For a fully discrete whole life insurance of 1000 issued to (x), y ou are given:
(i) (ii)
(iii)
2
Ax = 0.08 Ax = 0.2 The annual premium is determined using the equivalence principle.
S is the sum of the loss-at-issue random var
Homework Assignment 20:
(1)
On the basis of the Illustrative Life Table and an interest rate of 6%, calculate the annual benefit premium for a 2-year term life insurance that pays 1000 at the end of the year of death of (35). (Ans 1.9575)
(2) Exercise 6.1
Homework Assignment 19: (1) You are given the following information for a 3-year temporary life annuity-due issued to a life age x: Time t 0 1 2 Amount of Payment_ 1 2 3 px+t 0.80 0.75 0.50
Given that v = 0.9, calculate the actuarial present value of the
Homework Assignment 18: (1) Consider the following portfolio of annuities-due currently being paid from the assets of a pension fund. Age 65 75 85 Number of Annuitants 30 20 10
Each annuity has an annual payment of 1 as long as the annuitant survives. Ass
Homework Assignment 17: (1) You are given: (i) Ax = .28
(ii) (iii)
Ax+20 = .40
20
Ex = .25
(iv)
i = .05
Calculate the actuarial present value of a 20-year temporary life annuity-immediate of 1 at the end of each year for 20 years if (x) survives. (Ans 11.
Homework Assignment 16: (1) You are given:
k
0 1 2 3
k+1|
k| x
q
1.00 1.93 2.80 3.62
0.33 0.24 0.16 0.11
Calculate the actuarial present value of a 4-year temporary life annuity-due of 1 at the beginning of each year for 4 years if (x) survives. (Ans 2.22
Homework Assignment 15:
(1) For whole life insurances of 1000 on (65) and (66): (i) (ii) Death benefits are payable at the end of the year of death. The interest rate is 10% for 2008 and 6% for 2009 and thereafter. q65 = 0.010 and q66 = 0.012 The actuaria
Homework Assignment 14: (1) You are taking over the management of a fund. Exactly 20 years ago, the fund was set up to pay a death benefit of 1 to each of 10,000 lives age 65. You are given: (i)
(ii) (iii)
(iv)
The initial fund was 4,500. Mortality to dat
Homework Assignment 12: (1) You are given:
(i) (ii)
Mortality follows de Moivre's law. Var(T(15) = 675
Calculate . (Ans 105)
(2)
The Sesame Insurance Company issues a one-year policy to Big Bird promising to make a benefit payment at the end of the year a
Homework Assignment 11: (1) For a 2-year term life insurance with a unit benefit payable at the end of the year of death of a life age 50, you are given: (i)
(ii) (iii)
The actuarial present value of a 2-year pure endowment of 1 on a life age 50 is 0.840.
Homework Assignment 10: (1) Excel: Display the px, qx, and lx values of the Illustrative Life Table (Appendix 2A) in an Excel spreadsheet as described in Exercises 3.47 and 3.48. You do not need to hand in your spreadsheet, but give me the values you calc
Homework Assignment 9:
(1) Read When Non-Actuaries Play Actuary. Based on Table 3.3.1 in Chapter 3, calculate the number of years a person entering the labor force today at age 20 would expect to receive Social Security benefits. Assume retirement at 67.
Homework Assignment 8: (1) Do Exercise 3.7(e) on page 85. (2) Your company offers warranty coverage for MP3 players. The policy provides for the replacement of MP3 players that fail within 3 years of purchase of the MP3 player. The lifetime of a particula
Homework Assignment 7: Problems 1 and 2 are from the Exercises at the end of Chapter 3: (1) Exercise 3.7 (a), (b), (c), and (d) on page 85 (In this exercise you are given a survival function s(x), which represents the probability that a newborn will survi
Homework Assignment 6: (1) Iggy borrows X for 10 years at an annual effective rate of 6%. If he pays the principal and accumulated interest in one lump sum at the end of 10 years, he would pay 356.54 more in interest than if he repaid the loan with 10 lev
Homework Assignment 5: (1) Meredith deposits $12 into an account at the end of each day in 1989 and 1990 and $15 at the end of each day in 1991. The account earns 9% per year compounded annually in 1989 and 1990 and 12% per year compounded semiannually in
Homework Assignment 4:
(1) A man age 40 wishes to accumulate a fund for retirement by depositing $1000 at the beginning of each year for 25 years. Starting at age 65 he will make 15 annual withdrawals at the beginning of the year. Assuming that all paymen
Homework Assignment 25:
(1) For a fully discrete, 2-payment,3-year term insurance of 1,000 on a life age x, you are given: (i) i = 0.10 (ii) qx = 0.2, qx+1 = 0.25, qx+2 = 0.5 (iii) Expenses, paid at the beginning of the policy year, are: First Year Second
Homework Assignment 21: (1) A whole life insurance of 1, payable at the moment of death, is issued to a life age 50. The
single premium is 0.45. The probability that the present value of the financial loss is 0.150 is 0.200. A fully continuous whole life
STOR 471-Exam 2
November 12, 2012
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(1) Find the actuarial present value of each of the following insurances: (a) A 2-year term insurance that pays
STOR 372-Exam 2
November 14, 2011
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Print here: (1) You are given the following table of values for lx and Ax, assuming an annual effective interest rate of 6%.