ACTEX A C A D E M I C S E R I E S
Mathematics
of Investment
and Credit
5
th
Edition
SAMUEL A . BROVERMAN , PHD , ASA
UNIVERSITY O F TORONTO
ACTEX Publications , Inc.
Winsted, CT
Copyright 1991, 1996, 2004, 2008, 2010 by ACTEX Publications, Inc.
All rights
MATH 360: Theory of Investment and Credit
Albert Cohen
Actuarial Sciences Program
Department of Mathematics
Department of Statistics and Probability
C336 Wells Hall
Michigan State University
East Lansing MI
48823
[email protected][email protected]
Alb
Solutions Manual for
Mathematics
of Investment
and Credit
Th
Edition
SAMUEL A . BROVERMAN , PHD , ASA
Please, keep an attention!
I don t give you advise to use this type of illegal copy of this book.
I
ISBN: 978-1-56698-768 -L
9 781566 987684
Mathematic
MATH 320: Theory of Interest
January 9, 2017 (lecture 1)
Chapter 1: Interest rate Measurement
1.0 Introduction
The object of the book is to systematically develop insights and mathematical
techniques which lead to the fundamental principles upon which nan
MATH 320: Theory of Interest
January 12, 2017 (lecture 2)
Chapter 1: Interest rate Measurement
Finishing with section 1.4
Example:
Every Friday in February (the 7, 14, 21, and 28) Wait places a $1000 bet on credit. With
his bookmaker. The bookmaker charge
Exam FM
Adapt to Your Exam
INTEREST MEASUREMENT
INTEREST MEASUREMENT
Effective Rate of Interest
1
" =
1
1
= | = 1 + + 7 + =
H| = 1 + H|
Effective Rate of Discount
1
" =
MORE GENERAL ANNUITIES
MORE GENERAL ANNUITIES
Accumulation Fun
(xxx
MATH 320: Theory of Interest
January 17, 2017 (lecture 3)
From section 1.6, Force of interest
Example:
Suppose you deposit 5000 to an account that earns 5% annually for two years and
. . . 2
continuous interest With 5,: _ in subsequent years What has
MATH 329 HW 2 (due: 1/26/17) NAME . 1
Sufficient work must be shown to get credit for a correct answer. Partial credit may be given for incorrect
answers which have some positive work.
1. The accumulated value in J eff s account at time t is 100 + t and t
MATH 320: Theory of Interest
January 12, 2017 (lecture 2)
Chapter 1: Interest rate Measurement
Finishing with section 1.4
Example:
Every Friday in February (the 7, 14, 21, and 28) Walt places a $1000 bet on credit. With
his bookmaker. The bookmaker charge
MATH 320: Theory of Interest
January 19, 2017 (lecture 4)
Annuity-due : equal payments are made at the beginning of each period for n periods.
So the present value of an annuity-due with n level payments of 1 is:
a n | 1 v v 2 . v n 1
an |
1 vn 1 vn
1 v
MATH 320: Theory of Interest
January 17, 2017 (lecture 3)
From section 1.6, Force of interest
Example:
Suppose you deposit 5000 to an account that earns 5% annually for two years and
continuous interest with
in subsequent years. What has the account grown
L11 (2-21-2017)
Warm-up
1. If
i ( 4 ) .05
, find
A) 4.6%
d ( 2)
.
B) 4.7%
C) 4.8%
D) 4.9%
E) 5%
2. How much more interest (in dollars) is earned on an investment today of $1,000 during
the 4th year with effective annual compound interest of 5% than simple
MATH 320: Theory of Interest
January 31, 2017 (lecture 7)
Chapter 3 Loan Repayment
Section 3.1 Amortization of a Loan
Example
A loan of 1000 is made at the beginning of the year. Payments of 200 at the end of the
first year, 500 made at the end of the sec
L10 (2-16-2017) Amortization of a bond (for accounting purposes)
Example:
Complete the bond amortization schedule for a $1000 par value two-year bond maturing at par
with 8% coupons paid semiannually bought to yield 6% convertible semiannually.
solution:
MATH 320: Theory of Interest
January 26, 2017 (lecture 6)
Formulas:
sn|
(1 i) n 1
i
an|
(1 i ) n 1
sn |
d
1
a |
i
1 vn
i
1 vn
a n |
d
i
d
1 i
sn | s n | (1 i )
a |
and
i
1
d
d
1 d
a n | a n | (1 i )
Be able to recognize geometric series!
1 x x2 xk
Lecture 16 3/9/2017
Warm-up
1. For a 4-year 1000 par bond with 4% annual coupon use the yield curve to (i) calculate the
price of the bond and (ii) the annual effective rate in which the bond was bought.
Year
1
2
3
4
Spot rate
4%
4.5%
6%
7%
2. Project B r
MATH 320: Theory of Interest
January 24, 2017 (lecture 5)
Formulas:
sn|
(1 i) n 1
i
an|
(1 i ) n 1
sn |
d
i
d
1 i
1 vn
i
1 vn
a n |
d
and
i
1
a |
i
a |
d
1 d
sn | s n | (1 i )
a n | a n | (1 i )
Be able to recognize geometric series!
1 x x2 xk
Arit
Lecture 15 3/7/2017
Chapter 6.3: Forward rates of interest
The n-year forward rate is the rate agreed upon today for a one year loan to be made
n years in the future. One interpretation of a forward rate of interest is that it is the interest rate
that we
MATH 320: Theory of Interest
February 2, 2017 (lecture 8)
Chapter 3 Loan Repayment (continued)
Skip sections: 3.2.1 and 3.2.2
Also skip section 3.4
Section 3.3 The Sinking-Fund Method of Loan Repayment
When you use a sinking fund you make two payments: i)
L12 (2-23-2017)
Warm-up
1. Susan can buy a zero coupon bond that will pay 1000 t the end of 12 years and is
currently selling for 624.60. Instead, she purchase a 6% bond with coupons payable
semi-annually that will pay 1000 at the end of 10 years. She pai
MATH 320 HW 1 (due: 1/18/17)
NAME
Sufficient work must be shown to get credit for a correct answer. Partial credit may be given for incorrect
answers which have some positive work.
1. On December 16, Alex deposits 1000 into a savings account which pays or
Chapter 6: The term structure of interest rates
6.1 Spot rates and yield curves
Interest rates on loans depend in part on the time to maturity of the loan and the credit
rating of the borrower. For example, individuals looking for mortgage loans will gene
Lecture 17 3/14/2017
Warm-up
1. A 3-year annual coupon bond has coupons of 10 per year starting one year from now and
matures in 3 years for amount 100. The yield to maturity is 11.8% (effective annual).
Find the Macaulay duration for the bond.
2. (sectio
MATH 320: Theory of Interest
February 7, 2017 (lecture 9)
Formulas:
(1 i) n 1
sn|
i
1
a |
i
1 vn
an|
i
sn |
(1 i ) n 1
d
a n |
1 vn
d
sn|
(1 i ) n 1
an|
1 vn
a |
1
d
m
i (m)
e
(1 i ) 1
m
i
d
1 i
sn | s n | (1 i )
and
i
d
1 d
a n | a n | (1 i
L13 (2-28-2017)
Warm-up
1. A lender invests 20,000 to make a loan which will be repaid with 3 annual end of year
payments of 8,000. What is the yield of this investment?
2. An investment manager had a fund of 100,000 at the start of year 2006. On February
Associated Banc-Corp is a diversified bank holding company that provides banking and non-banking
services to individuals and businesses. They operate mainly in Wisconsin, Illinois, and Minnesota. Their
stock price fell sharply in 2008 and 2009, from $35.5
Chapter 18 Long-Term Debt Financing
Chapter Objectives:
Explain how an MNC uses debt financing in a manner that
minimizes its exposure to exchange rate risk,
Explain how an MNC assesses the potential benefits from
financing with a low-interest rate curr
Chapter 9 Forecasting Exchange Rates
Chapter Objectives:
Explain how firms can benefit from forecasting
exchange rates.
Describe the common techniques used for
forecasting.
Explain how forecasting performance can be
evaluated.
Explain how interval for