LEARNING OBJECTIVES FOR FIRST STOR 471 MIDTERM
I. Mathematical Interest Theory (65%)
A. Time Value of Money
1. Understand the following concepts:
Interest rate, discount rate, simple interest, compound interest, accumulation function,
amount function, fut

From email:
We have derived two actuarial formulas: (1) the prospective formula and (2) the
retrospective formula. The verbal form of the prospective formula states that
the benefit reserve is equal to the excess of the actuarial present value of the
futu

From email:
HW2 (3) The accumulated value after 5 years is A = 100(1 + .08/4) ^ (5*4) =
100(1.02)^20.
Now accumulate A five more years by multiplying it by (1 - .07)^(-5). So after 10
years you have B = 100 [(1.02)^20] [(.93)^(-5)].
Finally accumulate B f

From email:
The second STOR 471 midterm exam will be held on Monday, November 10 in 120
Hanes Hall from 5:30 until 7:30. It will cover the material in chapters 4 & 5 in our
textbook and homework sets 10-19.
The exam will be divided into 2 parts:
Part I (2

Homework Assignment 1:
(1) Sunmin deposits 10 into a fund today and 20 fifteen years later. Interest is credited at
a discount rate of d for the first 10 years and an interest rate of 6% thereafter. The
accumulated balance in the fund at the end of 30 yea

Homework Assignment 1:
(1) Sunmin deposits 10 into a fund today and 20 fifteen years later. Interest is credited
at a discount rate of d for the first 10 years and an interest rate of 6% thereafter. The
accumulated balance in the fund at the end of 30 yea

From email:
Solutions to the midterm exam are attached.
We now turn to the concept of a benefit reserve. Read the Introduction to
Chapter 7. It is saying that at time 0 the Equivalence Principle expresses an
actuarial equivalence between the future financ

From email:
The first 3 problems on this homework set involve the loss-at-issue random
variable L. For fully continuous insurances, L is defined by the middle columns of
Table 6.2.1 on page 173. For fully discrete insurances, L is defined by the middle
co

From email:
Solution to problem (1) on HW 21:
For the single premium insurance, L = (v ^ T) - .45
Pr(L >= .15) = Pr (v ^ T >= .60) = .2
For the fully continuous insurance, L = (v ^ T) P(a-bar-angle-T) = (1 +
P/delta)(v ^ T) (P/delta)
Pr(L >= .4) = Pr[v ^

From email:
In Table 15.2.3 the loss-at-issue random variable from Chapter 6 is extended to
include expenses. That is, outflow now includes expense payments along with
benefits. By setting the expected value of this new loss-at-issue random variable
equal

From email:
Please be aware that thedeadlineforresumesubmissionsforCignaisnextMonday,September
15th.Thisisearlierthaninpastyears.
On the first midterm you may be asked to express your answer in terms of
annuity symbols. Be sure that you are able to do thi

From the email:
The expression money grows at r% per year compounded
continuously means that the force of interest is numerically equal to
r%. It is very important that you understand this. In problem 3 on HW 5,
the force of interest is 5.4%.
Be sure you

From the email:
The solution to problem 3 on HW 6 proceeds as follows:
There are 180 payments in all, with payments 56-67 occurring in 1993.
Calculate loan payment. (2147.716532.)
Calculate OL after the 55th payment (based on 125 remaining payments). (203

From email:
Homework 18(3):
The present value random variable for each life is (15)(12)Y, where Y is
given by (5.4.1). The expected value of the PVRV is 180E(Y) and the variance is
(180^2)V(Y),where E(Y) and V(Y) are given by (5.4.2) and (5.4.4) with x=62

From email:
Increasing and decreasing annuities are introduced in Exercises 5.23 and
5.24 on page 161.
The actuarial present value of the apportionable annuity is developed in
section 5.5 on pages 154-155. Follow the books approach through the
first parag

From email:
Be sure you understand the actuarial notation (in bold print below) that is
used in the solutions to problems 4 & 5 on HW 4:
(4) The lady makes deposits more frequently than interest is compounded.
So the accumulated value of the deposits on S

From email:
Since we are normally given mortality data only for integer ages, we are faced
with the necessity of making some assumption in order to extrapolate the data
that we do not have. Many methods are possible, but there is one that is almost
always

From email:
A life insurance policy is a contract between an insurer and another party known
as the policyholder. In return for a payment of premiums, the insurer will pay a
predetermined amount of money known as the death benefit upon the death of
an ins

From email:
I gave everybody credit for the first problem on HW 10 because there was
a typo that made the problem unsolvable. HW 10 with the correction is
attached. Try to solve problem (1) if you haven't already done so. I will
give you the solution on W

From email:
ILT.xls (attached) contains the ps, qs and ls from the Illustrative Life
Table in Appendix 2A.
The calculations requested by problem (3) of HW 14 can be done in this
spreadsheet by adding a few more columns.
Today we explored the meaning of a

From email:
Note the quick solution to problem (5) on HW13. If somebody bought both
the increasing insurance and the decreasing insurance, the total death
benefit from the two policies would be 6 in every year. So IA + DA = 6A.
(4.4.4) on page 120 is an i

From email:
Solution to problem (2e) on HW 14:
ZB = v^(K+1), K<=9 and ZB = (1.207)v^(K+1),K>=10
Pr[v^(K+1) > .6 and K<=9] = Pr(K+1<8.77 and K<=9) = Pr(K<=7 and K<=9)
= Pr(K<=7) = 8q40=.0287
Pr[(1.207)v^(K+1) > .6 and K>=10] = Pr(K+1<11.995 and K>=10) =
Pr

From email:
The formulas for m-thly payment annuities are developed in section 5.4. The key
formulas for annuities-due are (5.4.11), (5.4.17) and (5.4.18). We derived them
in class by assuming uniform distribution of deaths within the year of age, so we
w

From email:
You might want to keep a copy of your solutions to HW 9, although hopefully you
will be able to pick up your solutions in the MDS Study Room before the exam on
Monday.
The article referenced in the first problem on HW 9 is attached to this ema

Csarrsn 1
THE MEASUREMENT OF MORTALITY
1. Introduction
The systematic analysis of the contingencies of human lii e forms
the foundation of an actuarys work. In the solution of problems
involving these contingencies, he requires some type of quantita
tive

(,)
()
()
L x
x
Tx
l x
d x = l x l x +1 = L x + L x +1 + L x + 2 + L
q x = d x / l x o
Tx
=
p x = l x +1 / l x
ex l x
()
()
()
xx+n
xn n q x
xn n p x
xx+nx+n+m n|m q x
l x+n l x+n+m
n|m q x =
lx
x

Homework Assignment 16:
(1) You
are given:
k
k+1|
k| x
q
0
1.00
0.33
1
1.93
0.24
2
2.80
0.16
3
3.62
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 2.2

Homework Assignment 12:
(1) For a one-year term insurance of 1000 payable at the end of the year of death of (50), you are
given:
(i) Z is the present value random variable for this insurance.
(ii) Mortality follows a life table where l50 = 8,457,616 and

Homework Assignment 10:
(1) You are given the following information from a life table:
(i)
x
lx
dx
px
qx
95
0.40
96
0.20
97
72
1.00
(ii)
l90 = 1000 and l93 = 825
(iii)
Deaths are uniformly distributed over each year of age.
Calculate the probability that

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 14:
(1) For a whole life insurance of 1000 on (50), you are given:
(i) The death benefit is payable at the end of the year of death.
(ii) Mortality follows the Illustrative Life Table.
(iii) i = 0.05 in the first year, and i = 0.06 in