University of Connecticut
Math 3615: Financial Mathematics Problems
Syllabus Spring 2016
Welcome to Math 3615!
This course is designed to help you prepare for the professional actuarial examination in
financial mathematics: the Society of Actuaries Exam F
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2011
Test 3 November 1, 2011
NAME
Do not open this test booklet until you are told to do so.
You will have 1 hour and 15 minutes to complete this test.
You must stop work as soon as
University of Connecticut
Math 3615: Financial Mathematics I
Fall 2012
QUIZ 3 09-24-13
Name _
1. You are given the following information about an investment account:
Date
January 1, 2011
April 1, 2011
January 1, 2012
Value Before
Deposit/Withdrawal
200
18
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Quiz 2 - 9/12/2013
Name
Solutions
1. Sharon makes annual deposits into an account at the beginning of each year for 20 years.
Sharons initial deposit is $100; each subsequent de
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2010
Test 3 October 28, 2010
NAME
DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE TOLD TO DO SO.
You will have 1 hour and 15 minutes to complete this test.
The test consists of 12 proble
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2010
Test 4 November 18, 2010
NAME
DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE TOLD TO DO SO.
You will have 1 hour and 15 minutes to complete this test.
The test consists of 12 probl
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2010
Test 2 October 12, 2010
NAME
DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE TOLD TO DO SO.
You will have 1 hour and 15 minutes to complete this test.
The test consists of 12 proble
University of Connecticut Math 3615: Financial Mathematics Problems Spring 2009 Test 4 April 23, 2009 ACTEX Modules 11-14
NAME
Only SOA-approved calculators are permitted in this test. No books or notes are permitted. Do not open this test booklet until y
University of Connecticut Math 3615: Financial Mathematics Problems Spring 2009 Test 3 April 5, 2009 ACTEX Modules 8-10, plus Section 7.8 in Module 7
NAME
Only SOA-approved calculators are permitted in this test. No books or notes are permitted. Do not op
University of Connecticut
Math 3615: Financial Mathematics Problems
Spring 2009
Test 3 April 5, 2009 - SOLUTIONS
ACTEX Modules 8-10, plus Section 7.8 in Module 7
1. You purchase 100 shares of Stock A on April 2, 2009, and sell the 100 shares on April 2,
2
University of Connecticut Math 3615: Financial Mathematics Problems Spring 2009 Test 2 March 5, 2009 ACTEX Modules 5 7 (plus end of Module 4)
NAME
Only SOA-approved calculators are permitted in this test. No books or notes are permitted. Do not open this
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2009
Test 3 October 29, 2009
NAME
Only SOA-approved calculators are permitted in this test.
No books or notes are permitted.
Do not open this test booklet until you are told to do so
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2009
Test 4 November 17, 2009
NAME
Only SOA-approved calculators are permitted in this test.
No books or notes are permitted.
Do not open this test booklet until you are told to do s
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2009
Test 3 October 29, 2009
NAME
Only SOA-approved calculators are permitted in this test.
No books or notes are permitted.
Do not open this test booklet until you are told to do so
University of Connecticut Math 280: Financial Mathematics Problems Spring 2008 Test 2 February 28, 2008
Please write your name in the space provided at the top of the next page.
Only SOA-approved calculators are permitted for this test. No books or notes
University of Connecticut Math 280: Financial Mathematics Problems Spring 2008 Test 4 April 24, 2008
NAME
Only SOA-approved calculators are permitted for this test. No books or notes are permitted. Do not open this test booklet until you are told to do so
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2009
Test 2 October 13, 2009
NAME
Only SOA-approved calculators are permitted in this test.
No books or notes are permitted.
Do not open this test booklet until you are told to do so
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Test 1 September 17, 2013
NAME
Solutions
1. A deferred annuity consists of 25 payments of 1,000 each.
A payment is made every 2nd year, with the first payment occurring at t=5.
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Test 2 October 8, 2013
NAME
Do not open this test booklet until you are told to do so.
You will have 1 hour and 15 minutes to complete this test.
You must stop work as soon as t
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University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 7
Asset-Liability Management, Duration, and Immunization
Duration (or Macaulay Duration) D or MacD
The duration of a stream of payments is a weighted average of the number
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 6
- TERM STRUCTURE OF INTEREST RATES Spot Rate (sn) the level annual interest rate that applies to a currently-issued n-year
zero-coupon bond
Yield Curve spot rates for zer
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 5
- YIELD RATE OF AN INVESTMENT To find the internal rate of return (IRR) for a series of cash flows, solve the following
equation for v:
C0 + C1v + C 2 v 2 + Cn v n = 0
Th
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 4
- BONDS Definitions:
F = face value or par value
r = coupon rate (per coupon payment period)
Fr = coupon amount
n = number of coupon payment periods remaining until redem
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 3
- LOAN REPAYMENT Outstanding Loan Balance
There are three methods for calculating the outstanding balance of a loan. The one to be
used in a particular situation depends
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 2
- ANNUITIES a + a r + a r 2 + . + a r n 1 = a
Finite Geometric series:
a + a r + a r 2 + . =
Infinite Geometric series:
1 rn
r n 1
= a
, where r 1
1 r
r 1
a
, where r <
Interest Functions
v=
1
(1 + i )
d = 1 v =
i=
i
= iv
1+ i
d
d
=
1 d v
i d = id
= ln(1 + i )
Accumulation function:
a (n) = (1 + i ) n = e n - for constant force of interest
n
(t ) dt
a (n) = e 0
- for variable force of interest
Definition of force of in
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Name
Homework Assignment 8 due Tuesday 11/19/13
1. A stock is currently trading at 105. The continuously compounded risk-free interest rate is
0.06. For each of the following si
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Name
Homework Assignment 6 due Tuesday 10/24/13
1. Stock A, a non-dividend-paying stock, traded at the following prices per share at each of the
indicated times:
Time
(in years)
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 1
- INTEREST RATES a(t) is the accumulation function; it represents the accumulated value at time t of an
investment of 1 unit that was made at time 0.
A(t) is the amount f