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Lecture 1
Introduction
Math 1140 Financial Mathematics
Ana Nora Evans403 [email protected]://people.virginia.edu/~ans5k/
Math 1140 - Financial Mathematics
Why do you take financial math?
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Math 1140 - Financial Mathematics
Easy A ?
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Homework
Class Participation
Project
Two Exams
Final
Math 1140 - Financial Mathematics
Project Ideas
• Federal Reserve System
• Explain the causes of a financial crisis
– Bank panic of 1907
– Savings and loans crisis
– 2008 financial crisis
• Analyze different options for a short term loan
• Explain the terms used in a “Mad Money” show
• Analyze a publicly traded company
• Build a stock portfolio
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Math 1140 - Financial Mathematics
Satisfy math requirement
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Become a financial guru
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Math 1140 - Financial Mathematics
Learn how to manage your finances
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COMM 2730 - Personal Finance
Math 1140 - Financial Mathematics
If you like this class, you may also like…
MATH 5140 - Mathematics of Derivative
Securities
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Beware
of prerequisites
Math 1140 - Financial Mathematics
Learn about…
How to calculate credit card interest
How to calculate loan interest
Annuities
Stock investing
Bonds
More precisely, most of chapters 1-7 from the
textbook.
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Additional Topics
Email me!
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Math 1140 - Financial Mathematics
Do you own a credit card?
A Yes
B No
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What is interest?
Interest is the fee paid by the borrower to
the owner.
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Interest rate is the percentage of the
amount borrowed charged to the
borrower for a fixed amount of time.
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Math 1140 - Financial Mathematics
APR
What is APR?
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Annual Percentage Rate
How do you calculate the interest rate per day?
365
APR
366
APR
360
APR
Math 1140 - Financial Mathematics
When do you think are you charged
interest for a credit card?
A) Every month, even if you pay the bill on time
B) When you don’t pay the entire bill
C) Only when you don’t pay the minimum
payment
D) None of the above
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Math 1140 - Financial Mathematics
What is the amount you pay interest
for?
A) Only the amount from previous cycle
B) The transaction from the previous and
current cycle
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Methods for Calculating Credit Card
Interest
Average daily balance
Adjusted balance
Previous balance
Two-cycle average daily balance
Daily accrual
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Math 1140 - Financial Mathematics
Daily Accrual
The interest is calculated daily, and billed at the end of each cycle.
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I = sum of daily interest
daily interest = daily balance * APR / 365
Math 1140 - Financial Mathematics
Example
Previous Balance: $2,500
Expenses and credits:
Day 1: $200
Day 10: $1,000
Day 20: -$1,000
Day 25: $500
APR: 13.24%
Cycle length: 30 days
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Math 1140 - Financial Mathematics
Daily Accrual
In our example:
Days 1-9: daily interest= $2,700 * 0.1324 / 365
= $0.97
Days 10-19: daily interest= $3,700 * 0.1324 / 365
= $1.34
Days 20-24: daily interest= $2,700 * 0.1324 / 365
= $0.97
Days 25-30: daily interest= $3,200 * 0.1324 / 365
= $1.16
I = 9 * $0.97 + 10 * $1.34 + 5 * $0.97 + 6 * $1.16 = $33.94
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Average Daily Balance
First we calculate the average daily balance.
add up the balance for each day and divide by the number of days
Calculate the interest per day
multiply the average daily balance with the daily
interest rate
Calculate the interest
multiply the daily interest by the number of days
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Math 1140 - Financial Mathematics
Average Daily Balance
I = ADB x APR x days in the billing cycle / 365
where
I is the interest
ADB is the sum of the balance of each day
in the cycle divided by the number of
days in the cycle.
APR interest rate per year
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Average Daily Balance
As a mathematical formula:
where
n is the number of days in the cycle
Bi is the balance on the ith day of the cycle
* ADB is my notation
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n
B
n
i
i∑=
=1
ADB
Math 1140 - Financial Mathematics
Example
I = ADB x APR x days in the billing cycle / 365
In our case:
ADB = $3,133.33
APR = 13.24%
days in the billing cycle = 30
I = $3,133.33 * 0.1324 * 30 / 365 = $34.09
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Adjusted Balance
I = (previous balance – payments) x APR x days in the billing cycle / 365
In our example:
previous balance = $2,500
payments = $1,000
I = ($2,500 - $1,000) * 0.1324 * 30 / 365
= $16.32
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Math 1140 - Financial Mathematics
Previous Balance
I = previous balance x APR x days in the billing cycle / 365
In our example:
previous balance = $2,500
I = $2,500 * 0.1324 * 30 / 365
= $27.20
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Two-cycle Average Daily Balance
I = ADB x APR x days in the billing cycle / 365
where
I is the interest
ADB is the sum of the balance of each day
in the current and previous cycle
divided by the number of days in the
two cycles.
APR interest rate per year
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Math 1140 - Financial Mathematics
Question
What do you think about the two-cycle
average daily balance method of
calculating interest?
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Office Hours
In 403 Kerchof Hall
Monday 1:00 – 2:30
Tuesday 3:30 – 5:00
By appointment
Email me if you have conflicts with both times
Feel free to stop by my office, but I might not be
there…
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Math 1140 - Financial Mathematics
Office Hours
What to do before coming to office hours
Read your class notes
Try to solve the homework by yourself
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I will ask for help. I will make a reasonable
effort to do things on my own first, but will
ask my classmates or the course staff for help
before getting overly frustrated.
Math 1140 - Financial Mathematics
Office Hours Don’t
Do not hang out in my
office
Do not do your homework
in my office.
Do not come in my office if
you are stopping by
unannounced and there
is a ‘Do not disturb’
notice on my door.
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Math 1140 - Financial Mathematics
Charge
Due Friday:
Read sections 1.2 and 1.3 and Syllabus
First homework
Signed course pledge
Registration Survey
Due Next Wednesday (31 August):
Second homework
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