Homework 2
Theory of Interest
Annuities immediate, due, deferred, continuous, perpetuities
1. Determine the present value of regular payments of $250 to be made at the end of
each of the next 50 years. The annual effective interest rate is 5%.
A. 3598
B.
Homework 3
Theory of Interest
Increasing and decreasing annuities
1. Max receives $300 in 1 year, $350 in 2 years, $400 in 3 years, and so on until the
final payment of $800. Using an annual effective interest rate of 4%, find the present
value of these p
Homework 8
April 1, 2016
(10 points) Assume the BlackScholes framework holds. You are given S0 =
100, = 25%, = 2%, r = 4%, K = 100, T = 1, N = 3. You are simulating
three paths of stock price movements based on the following numbers (assume
these are sam
Homework 9
April 18, 2016
1. (6 points) Suppose that the stock S is given by
dSt
= ( )dt + dZt
St
Apply Itos lemma to the following functions to obtain an expression for dF .
Simplify your answer as much as possible in terms of Ft , dZt , dt
(a) F (St , t
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The only surefire way to master the case interview
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SOCIETY OF ACTUARIES
EXAM MLC Models for Life Contingencies
EXAM MLC SAMPLE QUESTIONS
The questions in this study note were previously presented in study note MLC0908 and
MLC0911. The questions in this study note have been edited for use under the 201
W4440 Homework 2 Solution
Shuaiwen Wang
We can prove problem 2.18 first. Then the other problems.
Problem 2.1
Proof. Recall the formula for b0 and b1 :
Pn
b1 =
i=1 (Xi X)(Yi
Pn
2
i=1 (Xi X)
Y )
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i=1 Xi Yi nX Y
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n
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(think why)
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Theory of Interest
Class 1 Interest Rate & Factors
Prepared by Professor Noor Rajah
Revised by Duncan Szeto, FSA, MAAA
Chapter 1
Table of Content
Interest
Simple Interest
Compound Interest
Accumulated Value
Present Value
Rate of Discount
Constant F
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Last Name:
First Name:
UNI #:(=ABCD)
Quiz 5  K4830
Instruction: There are 2 questions in total, worth 10 points overall.
IMPORTANT: Please use YOUR OWN UNI to set up the problems, otherwise
you wont get points!
1. (6 points) Given the following Ito proce
K4830  Fall 2012  Final  December 20
SOLUTIONS
Problem (1). (20 points , no partial credit) Assume the BlackScholes framework holds.
You are given the following parameters:
S0 = 100,
K = 95,
r = 5%,
= 0.25,
T = 2.00,
= 2%
a. (4 points) Find the pric
Financial Mathematics
A Practical Guide for Actuaries
and other Business Professionals
By Chris Ruckman, FSA & Joe Francis, FSA, CFA
Published by BPP Professional Education
Solutions to practice questions Chapter 7
Solution 7.1
The bond pays annual coupon
Financial Mathematics
A Practical Guide for Actuaries
and other Business Professionals
By Chris Ruckman, FSA & Joe Francis, FSA, CFA
Published by BPP Professional Education
Solutions to practice questions Chapter 6
Solution 6.1
The annual effective yield
Financial Mathematics
A Practical Guide for Actuaries
and other Business Professionals
By Chris Ruckman, FSA & Joe Francis, FSA, CFA
Published by BPP Professional Education
Solutions to practice questions Chapter 5
Solution 5.1
The net present value is:
(
Homework 7
Theory of Interest
Duration/Convexity/Immunization/Term Structure of Interest Rates
1. The current price of a bond is $114.72 and the current yield is 6.00%. The
modified duration of the bond is 7.02. Use the modified duration to estimate the
p
Homework 4
Theory of Interest
Nonannual interest rates and annuities
1. Fill in the values in the following table:
 Effective Rate
Annual
(1 3.5%) 2 1 0.071225
SemiAnnual
7%/2=3.5%
Quarterly
(1 0.071225)1/4 1 0.01735
Monthly
(1 0.071225)1/12 1 0.00575
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