Lecture 7 Partial Payments Discount Interest
Transcript of Lecture 7 Partial Payments Discount Interest
Lecture 7
Partial Payments
Discount Interest
Ana Nora Evans 403 [email protected]://people.virginia.edu/~ans5k/
Math 1140 Financial Mathematics
Math 1140 - Financial Mathematics
Covers everything we do in
class, including Friday.
You must know: definitions,
formulas, applications.
Check page 39 from the
textbook.
Exam practice.
Credit card interest will not
be on the test (lecture 1
and part of lecture 2).
Quiz on Monday
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Math 1140 - Financial Mathematics
Survey ResultsThe pace is fast.
No one feels overworked
for now.
I should speak a little
louder for the people in
the back and not so loudly
for the people in the front.
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Math 1140 - Financial Mathematics
I will add more details to the examples
we solve in class.
I will give you more time to take notes.
I changed the slides style so the
question is up while we work on it.
But …
You must come prepared to class!
Go through examples by yourself and
come to office hours.
Start homework early!
Examples
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Someone hates that I
“don’t do enough practice
problems like the ones in
the homework”.
The homework should help
you understand the
material, not test your
ability to recognize patterns
and use a calculator.
Try the problems yourself
and come to office hours!
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“Some things are not
explained well. I feel like
the majority of the class
doesn’t understand some
of the stuff you try to
explain.”
I will try to add more
checkpoints to make sure we
are all on the same page.
Do something about it:
Come prepared for class.
Ask questions in class.
Come to office hours.
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How to prepare for class
Read the previous class.
Remember the definitions and
the formulas.
Solve the examples from class
by yourself.
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Questions?
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How much money will I have
in 6 months if I invest $100
at 5% simple interest?
S = P + I = P + Pit = P(1+it)
Future value at simple interest
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I have $100 today. The
value of my $100 three
days ago at 5% simple
interest was
A) $100
B) Less than $100
C) More than $100
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How much money do I
have to invest now at 5%
simple interest to have
$100 in 6 months?
How much money do I
need to invest today using
simple interest to have a
given amount at a future
date?
Present value at simple interest
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it
SP
+
=
1
Math 1140 - Financial Mathematics
For a simple interest loan, the
borrower is not required to
make any payments until the
due date.
The borrower and the lender
may agree how any partial
payments will reduce the
interest charges.
We are given:
the principal
the term
the partial payments
the dates the partial
payments are made
We calculate:
the balance on the
due date
Partial Payments
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The balance of a simple
interest loan with interest
rate i is the sum of the
payments, Q1, …, Qn
moved to the due date
using simple interest i, minus of the principal P moved to the due date
using simple interest I.
Merchant’s Rule
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Given
loan and due date
principal Pthe payments Q1, …, Qn
the dates of the payments
Want to calculate
balance on due date, which is
how much the borrower has
left to pay at the due date.
Math 1140 - Financial Mathematics
Merchant’s Rule
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Alice borrows $10 from Bob
for three years at an annual
interest rate 10%.
After one year Alice makes a
partial payment of $5 dollars.
After two year Alice makes a
partial payment of $2 dollars.
How much does Alice have to
pay at the due date? Use the
US rule.
Math 1140 - Financial Mathematics
United States Rule
The balance on the loan date is -P.
The new balance(at the payment date) is the sum
of the payment and the previous balance moved
to the payment date.
The balance on due date is the value of the
balance moved to the due date.
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United States Rule
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Alice borrows $10 from Bob
for three years at an annual
interest rate 10%.
After one year Alice makes a
partial payment of $5 dollars.
After two year Alice makes a
partial payment of $2 dollars.
How much does Alice have to
pay at the due date? Use the
US rule.
Math 1140 - Financial Mathematics
Using Merchant’s Rule
Alice has to pay $4.80 at
the due date.
Using US Rule is Alice has
to pay $5.06 at the due
date.
For a loan with interest rate i, principal P, partial payments Q1, …, Qn, and term t:A) The borrower always pays
more with the US Rule.B) The borrower sometimes
pays more with the Merchant’s Rule.
C) The borrower always pays more with the Merchant’s Rule.
D) The borrower always pays more with the Mob’s Rule.
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Math 1140 - Financial Mathematics
The correct answer is A.
The borrower always pays
more with the US Rule.
When using the US Rule, at
the first payment date we
add the interest to the
principal. That interest will
accrue interest.
When using the Merchant’s
Rule, the interest is
calculated at the end and no
interest on interest is paid.
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A) Crystal clear
B) I’m fine
C) Not so clear
D) I have no idea what
that is
Merchant’s Rule
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If you answered C, you should read section 1.7, Equations of Value, and
read the posted solutions for exercise 14 at page 26 from homework 3.
Math 1140 - Financial Mathematics
A) Crystal clear
B) I’m fine
C) Not so clear
D) I have no idea what
that is
US Rule
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Discount Interest
The interest is charged upfront.
Alice borrows today $500 from Shady Bank with a
10% discount rate.
Alice receives $450 from the back today.
One year from today Alice pays the back $500.
Why $450?
$500 - 10% x$500 x1 = $450
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Amount: S = $500
Discount: D = $50
Proceeds: P = $450
Discount rate:
d=10% per year
Term: t = 1 year
Discount Interest
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Amount = money borrowed
Discount = charge for the use of
money
Proceeds = money received from the
loan
Discount rate = percent of the
amount used to calculate the
discount
Term = length of the loan in units of
time
Math 1140 - Financial Mathematics
The Basic Discount Interest Formula
D = SdtWhere
D is the discount
S is the amount (future value)
d is the discount rate
t is the term
This is the formula for calculating the discount!
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P = S - DWhere
P is the proceeds
D is the discount
S is the amount (future
value)
P = S - D = S - Sdt= S(1-dt)
Discount Proceeds Formula
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Shady Bank charges 10%
for short-term discount
loans. What are the
proceeds for a six months
loan for $5,000?
Example
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A) Crystal clear
B) I’m fine
C) Not so clear
D) I have no idea what
that is
Discount Interest
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Next class
More on discount interest
Quiz Monday
Everything we covered up
then except credit card
interest.
Next Wednesday
Homework 4 is due.
First Exam (max 15 points):
26 September 2011 at 7pm
Location to be announced
Charge
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