Department of Statistics & Actuarial Science
Simon Fraser University
ACMA-210 Mathematics of Compound Interest
Sample Final Examination
1.
A used car dealership advertises the following arrangement:
We dont offer you confusing financing rates. Well just d
CHAPTER 4
BOND VALUATION
A bond is an interest-bearing debt security used to raise capital.
The bond issuer is the borrower
The bondholder (person who buys the bond) is the lender
Classification:
Maturity dates or perpetual (British Consols)
Callable
CHAPTER 6
THE TERM STRUCTURE
OF INTEREST RATES
In Chapter 5, we learned how to determine the price of a bond if the
face amount, term to maturity, coupon rate and yield rate are known.
Example 1:
Consider two bonds, each with face amount $100 and annual
c
SECTION 9.1
9.1.1
CHAPTER 9
(a) K: SoerT = 2000a = 2102.54.
(b) The no arbitrage price is $2102.54 (from part (a). A riskless
prot can be obtained in the following way:
(i) Take a short position on a one year forward contract
with forward (delivery) pri
CHAPTER 7
CASHFLOW DURATION
AND IMMUNIZATION
In the previous chapters we saw that the price of a fixed stream of
cash flows depends on the rate of interest used to value the stream.
As market rates of interest change, so do the prices of fixedincome inves
CHAPTER 1
INTEREST RATE MEASUREMENT
1.0 Definitions
may be defined as
person
for the use of an asset
belonging to another person
.
paid by one
It can be viewed as
that the borrower pays to the lender
for the use of the capital.
For this course, we will ex
7.2 Asset-Liability Matching and Immunization
A liability is an
An asset is a
a cash flow in the future.
a cash flow in the future.
Companies often back their liabilities with assets that are expected
to produce the same (or similar) cash flows as what th
CHAPTER 5
MEASURING THE RATE OF RETURN
OF AN INVESTMENT
5.1 IRR and NPV
Discounted cash flow analysis is the study of a stream of payments
taking into account the time value of money. The payments may have
a particular pattern (e.g. an annuity) or may be
4.3 Callable Bonds
A callable bond is one that can be
prior to its maturity
date at the
. The term of the bond is then uncertain.
The buyer should value the bond assuming that the seller (issuer)
will exercise the call option to the buyers disadvantage.
E
Simon Fraser University
Department of Stat. & Actu. Sci.
ACMA 425
Actuarial Mathematics II
Assignment 5 (Fall 2013)
Due time: 5pm, December 2, 2013
1. A universal life policy is sold to a 45 years old man. The initial premium is $2, 080 and the
ADB is a f
Simon Fraser University
Department of Stat. & Actu. Sci.
ACMA 425
Actuarial Mathematics II
Assignment 3
Due time: 5pm, November 7, 2013
1. You are given:
10 qx
= 0.15 and
30 qx
= 0.45;
10 py
= 0.90 and
30 py
= 0.50.
Find the following probabilities:
(a) t
Simon Fraser University
Department of Stat. & Actu. Sci.
ACMA 425
Actuarial Mathematics II
Assignment 4
Due time: 5pm, November 19, 2013
1. Exercise 9.2 on the textbook.
2. Exercise 9.5 on the textbook.
3. A special fully discrete insurance on (25) with l
Simon Fraser University
Department of Stat. & Actu. Sci.
ACMA 425
Actuarial Mathematics II
Solutions to Assignment 2 (Fall 2013)
= t px[Pt et + t V (St + Et )x+t ].
Here the rate of change of the benefit reserve under survivorship is the difference, under
Simon Fraser University
Department of Stat. & Actu. Sci.
ACMA 425
Actuarial Mathematics II
Solutions to Assignment 4 (Fall 2013)
58 +s59
1. (a) The members expected final average salary is 75, 000 s56+s574s+s
= $185, 265.
34
63+s64
(b) The expected averag
Simon Fraser University
Department of Stat. & Actu. Sci.
ACMA 425
Actuarial Mathematics II
Solutions to Assignment 1 (Fall 2013)
1. First you need to build a table for p[40] , p[40]+1 , p42 , . . . , p129, in which p[40] = 1 0.75q40,
p[40]+1 = 1 0.9q41. T
Simon Fraser University
Department of Stat. & Actu. Sci.
ACMA 425
Actuarial Mathematics II
Assignment 1
Due time: 5pm, October 1, 2013
1. Exercise 6.9 on the textbook.
2. A fully discrete 3-year endowment insurance is issued to (x). The benefit is equal
t
Simon Fraser University
Department of Stat. & Actu. Sci.
ACMA 425
Actuarial Mathematics II
Assignment 2
Due time: 5pm, October 15, 2013
1. Using the Thieles differential equation
d
(t V ) = t t V + Pt et (St + Et t V )x+t
dt
to write expressions for a)
d
1,2,6 Forcesgfulnterest
Another measure of interest is the IMEHSITYof the interest,
called the force of interest.
St is the force of interest applicable at time I and it is dened
as the relative rate of change in the amount function at that
time.
When t
._.,_
. IA. Nam.iual.Rates_9_fJInterest k W
Recall the effective annuai rate of interest:
i_ Mil-14(0) ; Wr ; 7, Me It) mlue ct
PINPa-l 1 M Van M SOTfDPOY
im
Investment A: 100 grows to 105 by the EOY '9 i = 5%
Note: time does not have to be measured in y
1.3 Equation of Value
Generally, we are interested in comparing two or more
streams of payments, or dated cash ows.
We might be given the cash ows and the rate of interest and
asked to choose between the two cash ows. .
OR
.we might be told that the two c
2.} Annujeswith NgqlConstant Pavments
_.+_.
(a). era! capws at. regular intervals
Suppose an amount C, is payable at time t (I = 0,1,2,.)-
0
t
PV0= Ct-Vt FV,=z Mfg-(Hun: itd-V"
0 O
Shortcut: use cashflow worksheet of a nancial calculator
g Cao
.L 6, 100 1
3.5 PracticalConsiderations
. f '00 WNW in own an
n i . . u
it) Iruth Ill Lending Act (US)
(onsun'icr (.redit Protection Act:
' 'Iille | of this Act is known as Truth in Lendingcwt
° Purpose: WM the terms of consumer loans
(nimlnq charge a; iinuna (mng ,K