ACTSC 331  Fall 2012  Assignment 2 SOLUTIONS
1. A contract issued to a life age x pays a sum insured of 10,000 immediately on death within
n years, and pays 20,000 on survival to n years. Level premiums are payable continuously
throughout the term of th
ACTSC 331  Life contingencies 1
Exercises (Chapter 7)
1. A fully continuous 20year payment, 30year term insurance of $2000 is issued to (35). We assume that
the force of interest of 6%, and the force of mortality is such that
t px
= exp
1:1x 1:1t
0:000
ACTSC 371 Corporate Finance 1
Instructor: Brent Matheson
Date: April 13, 2012
Time: 12:30 pm to 3:00 p.m.
Duration: 2.5 hours
Number of Pages: 19 including cover page, blank page, formula sheet and financial info
Aids: Calculator, attached formula sheet
F
ACTSC 331  Life Contingencies I
Test 1
1. (18 marks) Consider a special fully discrete whole life insurance with:
death benet payable at the end of the year of death: bK +1 = 400 e0:02(K +1) ,
premium
k
payable at time k (if survival):
k
=,
k = 0; 1; 2;
Review Notes ACTSC 331, FALL 2011
Part 1 Policy Values/Benet Reserves (Discrete Basis)
1. (Prospective/future) loss function or future loss random variable: A life insurance policy is issued to a life (x) or [x] (if the life is selected at age x). Given
t
Review Notes for Loss Models 1  ACTSC 431/831, Fall 2008 Part 1 Random Variables and Distributional Quantities
1. The distribution function (df ) or cumulative distribution function (cdf ) and survival function (sf ) of a random variable (rv) X are dened
ACTSCI 331  Life Contingencies I Exercises (Chapter 7)
1. A fully continuous 20year payment, 30year term insurance of 2000 is issued to (35). We assume that the force of interest is 6% and the force of mortality is given by (x) = 0:00005 1:1x (x > 0) w
ACTSC 331 Fall 2012 Assignment 3 SOLUTIONS
1. An insurer issues a 20 year level term insurance to a life aged exactly 60. The single
premium is paid at contract inception. The benet is 1.
(a) Suppose the death benet is paid at the year end. Write down and
ACTSC 331 Fall 2012 Assignment 4 SOLUTIONS
1. The gure below shows a shortterm model of employment/unemployment (so mortality
is ignored).
01 t
x+

Employed 0
Unemployed 1
10 t
x+
Assume that both transition intensities are constant, and that 01 t = and
ACTSC 331 Fall 2012 Assignment 3
due Friday Oct 26 at the beginning of class
1. An insurer issues a 20 year level term insurance to a life aged exactly 60. The single
premium is paid at contract inception. The benet is 1.
(a) Suppose the death benet is pa
ACTSC 331  Fall 2012  Assignment 2
Due Friday Oct 12 at start of class
1. A contract issued to a life age x pays a sum insured of 10,000 immediately on death within
n years, and pays 20,000 on survival to n years. Level premiums are payable continuously
ACTSC 331 Fall 2012 Assignment 4
due Friday Nov 9 at the beginning of class
1. The gure below shows a shortterm model of employment/unemployment (so mortality
is ignored).
01 t
x+

Employed 0
Unemployed 1
10 t
x+
Assume that both transition intensities
ActSc 371: Corporate Finance One
Assignment Four
Due December 3, at end of office hours
1. A stock has current price 100. Each year, the stock either has a return of 20%, or of
20%. The riskfree interest rate is 10% per annum.
a) Find the riskneutral p
ActSc 371: Corporate Finance One
Assignment One
Due October 10, at end of office hours
1. Consider the financial statements given below.
a) Determine the corporations cash flow.
b) Decompose the cash flow into the cash flow to shareholders and the cash fl
ActSc 371: Corporate Finance One
Assignment Three Answers
1. A company has a nominal discounting rate of 20%. By law it has to buy a machine to
sterilize the instruments used in its manufacturing process. It will buy one of two
machines, and once it has d
ACTUARIAL SCIENCE 371: CORPORATE FINANCE 1
Sample Final Exam
This is a sample final examination questions to give students an idea of how to prepare
the real final examination. Actual final exam may have both MC and WA types, but
here only WA type questio
Derivation of the Formula for Sustainable
Growth Rate
I use the notational convention
X = NewX OldX
(1)
Denoting EF N = External Funds Needed, we have:
EF N = New Assets (New Debt + New Equity)
(2)
And of course from the old balance sheet we have:
0 = Old
ActSc 371: Corporate Finance One
Assignment Two
1.Genco Inc. is an olive oil importer. Shares of similar risk to those of Genco have an
expected return in the market of 25%. Genco has earnings per share of $10, and paid all
its earnings as a dividend earl
ActSc 371: Corporate Finance One
Assignment Two
Due October 31, at end of office hours
1.Genco Inc. is an olive oil importer. Shares of similar risk to those of Genco have an
expected return in the market of 25%. Genco has earnings per share of $10, and p
ActSc 371: Corporate Finance One
Assignment Three
Due November 19, at end of office hours
1. A company has a nominal discounting rate of 20%. By law it has to buy a machine to
sterilize the instruments used in its manufacturing process. It will buy one of
ActSc 371: Corporate Finance One
Assignment Three
Due November 19, at end of office hours
1. A company has a nominal discounting rate of 20%. By law it has to buy a machine to
sterilize the instruments used in its manufacturing process. It will buy one of
ActSc 371: Corporate Finance One
Assignment One
1. Consider the financial statements given below.
a) Determine the corporations cash flow.
b) Decompose the cash flow into the cash flow to shareholders and the cash flow to
bondholders.
Income Statement 200
ACTSC 331  Fall 2012  Assignment 1 SOLUTIONS
1. Show that the distribution of Tx tTx > t is equal to the distribution of Tx+t . (This
is what we apply when we write Lt in terms of Tx+t instead of as a conditional rv.)
We will nd the survival function o
ACTSC 331  Fall 2012  Assignment 1
Due Friday September 28 at start of class
1. Show that the distribution of Tx tTx > t is equal to the distribution of Tx+t . (This
is what we apply when we write Lt in terms of Tx+t instead of as a conditional rv.)
2.
ACTSC 331  Life Contingencies I
Test 2
1. (5 marks) A special fully discrete 2year term life insurance is issued to (63). The death benet
payable at the end of the year of death and the premium payable at the beginning of the year are
dened as follows: