Lecture 2 Simple Interest Ana Nora Evans 403 Kerchof
[email protected] http://people.virginia.edu/~ans5k/ Math 1140
Financial Mathematics
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Math 1140 - Financial Mathematics First Homework 2 Turn it in
now!!! No late homework is accepted, unless you asked for an
extension before and I agreed.
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Math 1140 - Financial Mathematics Questions 3 Syllabus Last
class
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Math 1140 - Financial Mathematics Class Participation Ask
questions Answer questions Clickers 4
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Math 1140 - Financial Mathematics Types of clicker questions
Anonymous You get 2 points for answering. I dont see your answer.
Participation You get 2 points for answering. I will see your
answer. Correct/Incorrect You get 2 points for an incorrect answer.
You get 3 points for an correct answer. 5
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Math 1140 - Financial Mathematics Are you awake? A)Yes B)No
This is an anonymous question. 6
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Math 1140 - Financial Mathematics Collab I put the
participation grades in Collab. I gave maximum credit to everybody
that participated in the first class. 7
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Math 1140 - Financial Mathematics What do you think about the
class? 8 A)I would like to drop the class, but I cant B)I plan to
drop the class C)I love the class and plan to stay D)I plan to take
a nap during class E)I dont care about anything This is an
anonymous question.
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Math 1140 - Financial Mathematics Last Time 9 We started to
learn about credit cards. Interest Interest Rate Methods for
calculating interests Daily Accrual Average Daily Balance
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Math 1140 - Financial Mathematics What is interest? A)An amount
of money you pay to borrow money B)A percentage C)A time interval
D)The amount of money you borrow This is a correct/incorrect
question. 10
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Math 1140 - Financial Mathematics Today Brief review of the
first lecture Talk about second homework Start Simple Interest
11
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Math 1140 - Financial Mathematics Math is easy, life is messy
12 Flickr cc:bitzcelt
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Math 1140 - Financial Mathematics What is interest? Interest is
the fee paid by the borrower to the owner. 13 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 Simple Interest I = Pit I =
interest (Cost for the use of the borrowed money) P = principal
(Amount of money borrowed) i = interest rate (Percent of the
principal that is the basis for the interest for a given time
period) t = term (Length of the loan in time units) 14
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Math 1140 - Financial Mathematics Maturity Value S = P + I S =
maturity value (future value, amount) The amount of money a
borrower will pay back. 15
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Math 1140 - Financial Mathematics What does this mean? Alice
borrows from Bob $100 for one year with 14% per year interest. How
much money does Alice pay in interest? 16 Bob gives Alice $100
today, 26 August 2011. On 26 August 2012, Alice gives back $100
plus the interest. The interest is 14% of $100.
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Math 1140 - Financial Mathematics What is %? What does 14%
mean? A)0.14 B)1.4 C)14 D)0.014 E)140 17
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Math 1140 - Financial Mathematics What about 0.02%? A)2 B)0.02
C)0.0002 D)20 E)200 18
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Math 1140 - Financial Mathematics From words to formula Alice
borrows from Bob $100 for one year with 14% per year interest. How
much money does Alice pay in interest? Given: principal: P =
interest rate: i = term: t = Unknown (what we need to calculate):
interest: I = 19
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Math 1140 - Financial Mathematics What about days? Bob wants to
earn 14% per year for its money. Alice wants $100 for one day.
Given: principal: P = interest rate: i = term: t = Unknown (what we
need to calculate): interest: I = 20
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Math 1140 - Financial Mathematics Back to money Bob wants to
earn 14% per year for its money. Alice wants $100 for one day.
interest rate: i = interest: I = 21
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Math 1140 - Financial Mathematics Were did we see this before?
APR = annual percentage rate = a percentage, like 14% How do you
calculate the interest rate per day? annual rate = per year
interest rate = APR per year = APR / 365 per day 22
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Math 1140 - Financial Mathematics We saw I = Pit last time 23 I
= sum of daily interest daily interest = daily balance * APR / 365
I = ADB x APR x days in the billing cycle / 365
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Math 1140 - Financial Mathematics Daily Accrual daily interest
= daily balance * APR / 365 I = P = i = t = 24
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Math 1140 - Financial Mathematics Average daily balance The
interest is: ADB x APR x days in billing cycle / 365 I = P = i = t
= 25
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Math 1140 - Financial Mathematics Math is POWER You need to
know one formula I = Pit And units of measurement conversion 1 year
= 365 days Multiplication and division 26
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Math 1140 - Financial Mathematics Life is complicated Why makes
the formulas look so different? 27 The principal! For daily
accrual: P = day balance For average daily balance: P = average
daily balance
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Math 1140 - Financial Mathematics 28
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Math 1140 - Financial Mathematics There is a bit more math here
Average Daily Balance?!!!!! 29
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Math 1140 - Financial Mathematics Simple Interest Home equity
loans Promissory notes Bonds 30
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Math 1140 - Financial Mathematics What is missing? Mortgage
Credit card loans 31 I only told you how to calculate interest for
one billing cycle! At the end of the cycle the interest is added to
the balance. Next cycle the borrower pays interest on
interest!
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Math 1140 - Financial Mathematics Compound interest Well talk
about it in a few weeks. Assuming the same interest rate, for which
type of interest the borrower pays more: A)Simple interest
B)Compound interest This is a participation question. 32
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Math 1140 - Financial Mathematics Simple vs Compound Interest
Simple interest grows linearly. Compound interest grows
exponentially. 33
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Math 1140 - Financial Mathematics Second Homework First problem
Understand what real credit cards do Second and third problems Easy
applications of average daily balance method 34
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Math 1140 - Financial Mathematics Last Problem We have not
covered enough to solve it! If you know it already, take a golf
class! But first tell me the answer. What I want you to do? Think!
Use a search engine (Google, duckduckgo, Bing)! 35
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Math 1140 - Financial Mathematics Last Problem Nora has a
pressing $22,000 financial need. She can use one of the following
methods to pay it: Credit card loan with APR= 16.24% and using
average daily balance method Margin loan with 9% per year interest
rate and using daily accrual interest (compounded monthly). Sell
stock. Assume a return on investment of 14.32%. She can pay back
$3,000 monthly. Which method is the most advantageous for her to
use to pay the $22,000? 36
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Math 1140 - Financial Mathematics Suggestions Use a search
engine to find interest calculators. Is one method obviously wrong?
Think about capital gains tax. Is the return on investment
realistic? What are the risks of owning stock? 37
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Math 1140 - Financial Mathematics Another example Guido the
Enforcer offers you a simple interest loan of $1,000 at 3% weekly
rate. Is this a good deal or a bad one? A)Really good B)Good C)Bad
D)Run as fast as you can This is a participation question. 38
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Math 1140 - Financial Mathematics Lets calculate Guido the
Enforcer offers you a simple interest loan of $1,000 at 3% weekly
rate. 39
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Math 1140 - Financial Mathematics What is the interest per
year? 40
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Math 1140 - Financial Mathematics Other types of problems Given
the interest, the interest rate and the term of a simple interest
rate, what is the principal? 41
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Math 1140 - Financial Mathematics Other types of problems What
is the formula for interest rate? What is the formula for the term?
42
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Math 1140 - Financial Mathematics Next time More about simple
interest I will continue with section 1.3 43
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Math 1140 - Financial Mathematics Charge Due Monday: Read
sections 1.3 and 1.4 Due Next Wednesday (31 August): Second
homework 44
