Math 1140 Financial Mathematics Why do you take financial

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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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Easy A ?

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Homework

Class Participation

Project

Two Exams

Final


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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Satisfy math requirement

5Math 1140 - Financial Mathematics

Become a financial guru

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Learn how to manage your finances

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COMM 2730 - Personal Finance


If you like this class, you may also like…

MATH 5140 - Mathematics of Derivative

Securities

8

Beware

of prerequisites


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.


Additional Topics

Email me!

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Do you own a credit card?

A Yes

B No


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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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


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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What is the amount you pay interest

for?

A) Only the amount from previous cycle

B) The transaction from the previous and

current cycle


Methods for Calculating Credit Card

Interest

Average daily balance

Adjusted balance

Previous balance

Two-cycle average daily balance

Daily accrual

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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


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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Daily Accrual

In our example:

Days 1-9: daily interest= $2,700 * 0.1324 / 365

= $0.97


= $1.34


= $0.97


= $1.16

I = 9 * $0.97 + 10 * $1.34 + 5 * $0.97 + 6 * $1.16 = $33.94


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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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



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


Example


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


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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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


Two-cycle Average Daily Balance


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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Question

What do you think about the two-cycle

average daily balance method of

calculating interest?


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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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.


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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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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Documents

Math 1140 Financial Mathematics Why do you take financial