A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2
Marcel B. Finan Arkansas Tech University c All Rights Reserved Preliminary Draft Last Updated 11/02/08
2
In memory of my mother August 1, 2008
Pref
MATH 320
HOMEWORK 7
Due Wednesday, October 20
1. A thirtyyear annuityimmediate makes annual payments. The rst 10 payments are of amount 100. The payments then decrease by 5 each year until the 20th payment, which is of amount 50. The last 10 payments ar
MATH 320
HOMEWORK 5
Due Wednesday, September 29
1. A perpetuity pays 1 at the end of every year plus an additional 1 at the end of every second year. The present value of the perpetuity is K for i 0. Determine K in terms of i (simplify!) 2. Annual deposit
MATH 320
HOMEWORK 4
Due Wednesday, September 22
1. Chris lends Dennis X at a rate of 12% per annum eective, at time t = 0. Dennis is to repay in three installments: 22.40 at t = 1, 28.10 at t = 3, and 15.74 at t = 4. (a) What is X? (b) The repayments are
MATH 320
HOMEWORK 3
Due Wednesday, September 15
1. Annual compound interest rates are 13% in 1984, 11% in 1985, and 15% in 1986. Find the eective rate of compound interest per year which yields an equivalent return over the threeyear period. 2. suppose t
MATH 320
HOMEWORK 2
Due Wednesday, September 8
1. An investment worth $500 on January 1, 1990, is worth $600 on January 1, 1992. What is its value (a) On January 1, 1993, assuming simple interest (b) On January 1, 1993, assuming compound interest (c) On J
Math 320, Mathematics of Interest
Homework # 2
Homework due Friday Sept 16 by 5pm
You can work in small groups, but everybody should turn in his/her own
solution sheet. Please show all the work, so that the partial credit can be
given if necessary. Answer
IT26
PRACTICE MULTIPLE CHOICE TEST 7
1.
Investment X for 100,000 is invested at a nominal rate of interest, j, convertible semiannually. After four years it accumulates to 214,358.88. Investment Y for 100,000 is invested at a nominal rate of discount, k,
II22
PRACTICE MULTIPLE CHOICE TEST 6
1.
Fund A accumulates at a force of interest 1 +0.~5t at time accumulates at a constant force of interest .05. You are given: (i) The amount in Fund (ii) The amount in Fund (iii) The amount in Fund Fund A and Fund B.
II19
PRACTICE MULTIPLE CHOICE TEST 5
1.
You are given 8t = t ~ 1 for 2:; t ~ 10. For anyone year interval between nand with 2 :; n :;9, calculate the equivalent d(2). (B)
n + 1,
l n
(C)
nn 
1
(D) n1
_n_
,'
2.
The accumulated value of 1 at time t, for 0
ITIS
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:~
PRACTICE MULTIPLE CHOICE TEST 4
11 .,
,
~r
2.
You are given
in atidt
(B)
= 100.
nO
Calculateanj'
(A) 100nO
(C;
n  1000
(D) 100 
nO
(E)
n  100
o
In Fund A, the accumulated value of 1 at any time t > 0 is 1 + t. In Fund B, the accumulated val

.~._~_
IIll
.
,
PRACTICE MULTIPLE CHOICE TEST 3
1.
A loan of 1000 is made at an interest rate of 12% compounded quarterly. The loan is to be repaid with three payments: 400 at the end of the first year, 800 at the end of the fifth year, and the bala
MATH 320
HOMEWORK 1
Due Wednesday, September 1
1. I invest $1000 on January 1, 1995. By January 1, 1996, my investment is worth $1200. The time unit is years. Write down A(0), A(1), and a(1) in the following three cases: (a) The money unit is $1 (b) The m



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The Theory of Interest  Solutions Manual
Chapter 3
1. The equation of value using a comparison date at time t = 20 is 50,000 = 1000s20 + Xs10 at 7%. Thus, 50, 000 1000s20 50,000 40,995.49 = = $651.72. X= s10 13.81645 2. The down payment (D) plus the amou
The Theory of Interest  Solutions Manual
Chapter 2
1. The quarterly interest rate is
i 4 .06 = = .015 4 4 and all time periods are measured in quarters. Using the end of the third year as the comparison date j=
()
3000 (1 + j ) + X = 2000v 4 + 5000v 28 X
The Theory of Interest  Solutions Manual
Chapter 1
1. (a) Applying formula (1.1)
A ( t ) = t 2 + 2t + 3 so that
and A ( 0 ) = 3
a (t ) =
A(t ) A(t ) 1 ( 2 = = t + 2t + 3) . k A (0) 3
(b) The three properties are listed on p. 2. (1)
1 a ( 0 ) = ( 3) = 1.
MATH 320
HOMEWORK 6
Due Wednesday, October 6
1. An annuity consists of n payments of 1, the rst to be made at the end of 7 years and the others to be made at three year intervals thereafter. The rate of interest is i per annum eective. Derive an expressio