Lecture 1 Introduction Math 1140 Financial Mathematics Ana Nora Evans 403 Kerchof [email protected] ans5k

Lecture 1 Introduction

Math 1140 Financial Mathematics

Ana Nora Evans403 [email protected]://people.virginia.edu/~ans5k/

2Math 1140 - Financial Mathematics

Why do you take financial math?


Easy A ?HomeworkClass Participation ProjectTwo 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


Satisfy math requirement


Become a financial guru


Learn how to manage your finances

COMM 2730 - Personal Finance


If you like this class, you may also like…

MATH 5140 - Mathematics of Derivative Securities

Bewareof prerequisites


Learn about…

How to calculate credit card interestHow to calculate loan interestAnnuitiesStock investingBondsMore precisely, most of chapters 1-7 from the

textbook.


Additional Topics

Email me!


Do you own a credit card?

A Yes B No


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.


APR

What is APR?

Annual Percentage Rate

How do you calculate the interest rate per day?

365

APR

366

APR360

APR


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


What is the amount you pay interest for?

A) Only the amount from previous cycleB) The transaction from the previous and

current cycle


Methods for Calculating Credit Card Interest

Average daily balanceAdjusted balancePrevious balanceTwo-cycle average daily balance Daily accrual


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


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


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



= $1.16I = 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 rateCalculate the interest

multiply the daily interest by the number of days



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



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


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


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


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

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


Question

What do you think about the two-cycle average daily balance method of calculating interest?


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…


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.


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.


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

Documents

Lecture 1 Introduction Math 1140 Financial Mathematics Ana Nora Evans 403 Kerchof [email protected] ans5k