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

2


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.

3


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

4


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!

5


“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.

6


How to prepare for class

Read the previous class.

Remember the definitions and

the formulas.

Solve the examples from class

by yourself.

7


Questions?

8


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

9


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

10


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

11

it

SP

+

=

1


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

12


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

13

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.


Merchant’s Rule

14

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


How much does Alice have to

pay at the due date? Use the

US rule.


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.

15


United States Rule

16

Alice borrows $10 from Bob

for three years at an annual

interest rate 10%.

After one year Alice makes a


After two year Alice makes a


How much does Alice have to

pay at the due date? Use the

US rule.


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.

17


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.

18


A) Crystal clear

B) I’m fine

C) Not so clear

D) I have no idea what

that is

Merchant’s Rule

19

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.


A) Crystal clear

B) I’m fine

C) Not so clear


that is

US Rule

20


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

21


Amount: S = $500

Discount: D = $50

Proceeds: P = $450

Discount rate:

d=10% per year

Term: t = 1 year

Discount Interest

22

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


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!

23


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

24


Shady Bank charges 10%

for short-term discount

loans. What are the

proceeds for a six months

loan for $5,000?

Example

25


A) Crystal clear

B) I’m fine

C) Not so clear


that is

Discount Interest

26


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

27

lecture 7 partial payments discount interest

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