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Transcript of Lecture 1 Introduction Math 1140 Financial Mathematics Ana Nora Evans 403 Kerchof...
Lecture 1 Introduction
Math 1140 Financial Mathematics
Ana Nora Evans403 [email protected]://people.virginia.edu/~ans5k/
4Math 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
8Math 1140 - Financial Mathematics
If you like this class, you may also like…
MATH 5140 - Mathematics of Derivative Securities
Bewareof prerequisites
9Math 1140 - Financial Mathematics
Learn about…
How to calculate credit card interestHow to calculate loan interestAnnuitiesStock investingBondsMore precisely, most of chapters 1-7 from the
textbook.
12Math 1140 - Financial Mathematics
What is interest?
Interest is the fee paid by the borrower to the owner.
Interest rate is the percentage of the amount borrowed charged to the borrower for a fixed amount of time.
13Math 1140 - Financial Mathematics
APR
What is APR?
Annual Percentage Rate
How do you calculate the interest rate per day?
365
APR
366
APR360
APR
14Math 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 timeB) When you don’t pay the entire billC) Only when you don’t pay the minimum
paymentD) None of the above
15Math 1140 - Financial Mathematics
What is the amount you pay interest for?
A) Only the amount from previous cycleB) The transaction from the previous and
current cycle
16Math 1140 - Financial Mathematics
Methods for Calculating Credit Card Interest
Average daily balanceAdjusted balancePrevious balanceTwo-cycle average daily balance Daily accrual
17Math 1140 - Financial Mathematics
Daily Accrual
The interest is calculated daily, and billed at the end of each cycle.
I = sum of daily interest
daily interest = daily balance * APR / 365
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Example
Previous Balance: $2,500Expenses and credits:
Day 1: $200Day 10: $1,000Day 20: -$1,000 Day 25: $500
APR: 13.24%Cycle length: 30 days
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Daily Accrual
In our example:Days 1-9: daily interest= $2,700 * 0.1324 / 365
= $0.97Days 10-19: daily interest= $3,700 * 0.1324 / 365
= $1.34Days 20-24: daily interest= $2,700 * 0.1324 / 365
= $0.97Days 25-30: daily interest= $3,200 * 0.1324 / 365
= $1.16I = 9 * $0.97 + 10 * $1.34 + 5 * $0.97 + 6 * $1.16 = $33.94
20Math 1140 - Financial Mathematics
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 rateCalculate the interest
multiply the daily interest by the number of days
21Math 1140 - Financial Mathematics
Average Daily Balance
I = ADB x APR x days in the billing cycle / 365where
I is the interestADB 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
22Math 1140 - Financial Mathematics
Average Daily Balance
As a mathematical formula:where
n is the number of days in the cycleBi is the balance on the ith day of the
cycle * ADB is my notation
n
Bn
i
i 1 ADB
23Math 1140 - Financial Mathematics
Example
I = ADB x APR x days in the billing cycle / 365
In our case:ADB = $3,133.33APR = 13.24%days in the billing cycle = 30
I = $3,133.33 * 0.1324 * 30 / 365 = $34.09
24Math 1140 - Financial Mathematics
Adjusted Balance
I = (previous balance – payments) x APR x days in the billing cycle / 365
In our example:previous balance = $2,500payments = $1,000
I = ($2,500 - $1,000) * 0.1324 * 30 / 365 = $16.32
25Math 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
26Math 1140 - Financial Mathematics
Two-cycle Average Daily Balance
I = ADB x APR x days in the billing cycle / 365where
I is the interestADB 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
27Math 1140 - Financial Mathematics
Question
What do you think about the two-cycle average daily balance method of calculating interest?
28Math 1140 - Financial Mathematics
Office HoursIn 403 Kerchof Hall
Monday 1:00 – 2:30Tuesday 3:30 – 5:00
By appointment
Email me if you have conflicts with both timesFeel free to stop by my office, but I might not be
there…
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Office HoursWhat to do before coming to office hours
Read your class notesTry to solve the homework by yourself
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.
30Math 1140 - Financial Mathematics
Office Hours Don’tDo not hang out in my
officeDo 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.