Chapter 11a Summary
Mark Krilanovich
©March 1, 2009
BUS 103
Simple Discount Notes
Definitions:
1. What is a "Note"?
a. When you borrow money, you sign a "Note" promising to pay it back.
b. It is often called a "Promissory Note" because it promises that you will pay.
c. After you sign it, you give to the person you borrowed from (the lender).
2. What does a Promissory Note say?
a. The Date of the Note specifies when you borrowed the money.
b. The Duration of the Note specifies how much time until you will pay it back.
c. The Discount Rate (percent per year) implies how much of a fee you will pay
the lender.
d. The Face Value of the note, the amount of money you will pay back.
3. How does the borrowing process work?
a. When you borrow, the lender hands you some money, your Proceeds.
b. At the maturity date, you pay the lender back more money, the Maturity Value.
c. The difference is the lender's fee (Bank Discount, in dollars) for letting you use
his money
4. What are the two kinds of Promissory Notes?
a. Simple Interest Note (in Ch. 10): the Face Value equals your Proceeds, and
the Maturity Value that you repay equals your Proceeds plus the lender's
interest.
b. Simple Discount Note (in Ch. 11): the Face Value equals the Maturity Value,
and your Proceeds equals the Face Value minus the lender's interest (Bank
Discount).
c. Either way, you pay back more than you borrowed; that's life. The only real
difference is the definition of the words.
d. (The textbook says for a Simple Interest Note, "You pay the Interest at the end,"
whereas for a Simple Discount Note, "The lender deducts the interest at the
beginning." That's true. If it helps you to think of it that way, that's fine.)
5. Sometimes a Simple Discount Note is called a "noninterest-bearing note." Ignore the
word "noninterest-bearing."
6. (You don't need to understand the word "discount." It's just a word.)
Formulas to use:
1. Bank Discount = (Face Value) x (Bank Discount Rate) x (Duration of Note)
2. Maturity Value = Face Value
[what you pay back at the end]
3. Proceeds = Maturity Value - Bank Discount [what you receive at the beginning]
4. Effective Rate = (Bank Discount) / [(Proceeds) x (Duration of Note)]
[This comes from Chapter 10's famous Interest = Principal x Rate x Time.
This "effective rate" is what the lender actually earns by lending you money.]
©2009 by Mark Krilanovich
This and many other handouts are available at www.silcom.com/~mkrilano
Chapter 11, page
2
Procedure to work problems:
1. Always show all your work.
2. Draw a time line.
3. Label the beginning (Date of Note) and end (Maturity Date) of the time line.
4. Show what you will be trying to find (solve for).
5. Use the four formulas above, choosing the one(s) you need.
6. Solve for the number(s) you need to find.
7. Check: does your answer make sense?
Example Problem A:
Face Value=$30,000
Discount Rate=7%
Maturity Value=?
| ------------------------------------------------------------- |
Duration of Note=6 months
Date of Note
(1) Bank Discount =
=
=
=
Maturity Date;
Proceeds=?
(Face Value) x (Bank Discount Rate) x (Duration of Note)
($30,000) x (7%/year) x [(6 months) / (12 months/year)]
($30,000) x (.07/year) x (.5 years)
$1050
(2) Maturity Value = Face Value
= $30,000
(3) Proceeds = Maturity Value - Bank Discount
= $30,000 - $1050
= $28,950
(4) Effective Rate =
=
=
=
=
(Bank Discount) / [(Proceeds) x (Duration of Note)]
($1050) / [($28,950) x (6 months/12 months/year)]
($1050) / ($14,475)
.072539 (per year)
7.25% (per year)
Always show all your work.
©2009 by Mark Krilanovich
This and many other handouts are available at www.silcom.com/~mkrilano
Chapter 11, page
3
Chapter 11b
"Discounting" a Promissory Note Before Maturity
A change in gears:
1. The first part of this chapter dealt with business between two people: the lender
and the borrower. This part deals with business between three parties: the lender,
the borrower, and a bank.
2. The first part of this chapter dealt with two dates in history: the date of the loan,
and the date of repayment of the loan (the maturity date). This part deals with
three dates in history: the date of the loan, the "discount date," and the date of
repayment of the loan (maturity date).
3. The first part of this chapter dealt with a "simple discount promissory note." This
part deals instead with the "simple interest promissory note" that we learned in
Chapter 10.
4. This part of the chapter talks about a process called "discounting," but the note is
not a discount note; it's a simple interest note, as point (3) said. See below for
the meaning of this "discounting" process.
What's happening here?
1.
2.
3.
4.
5.
First, you lend money to a borrower for a certain length of time.
The borrower signs a simple interest note, and gives it to you.
Next, before the maturity date, you decide you want some money.
You sell the note to a bank, before its maturity date.
The bank gives you some money, but less than the borrower will repay at the
maturity date.
6. That's because the bank charges you a fee for this service.
7. Next, the bank holds the note until its maturity date.
8. Last, the original borrower pays the bank the full amount he would have paid you if
you had kept the note. (The borrower pays the same amount either way, so he
doesn't care whom he pays. The bank receives more money than it gave you, so it
has happily earned some income.)
Definitions:
1. The following are the same as in Chapter 10:
a. The borrower borrows the Principal ("Face Value") on the Date of the Note.
b. On the Due Date, the borrower repays the Maturity Value.
c. The Interest = Principal x Interest Rate x Time Length of Note.
d. The Maturity Value = Principal + Interest.
2. These are new in Chapter 11 for "discounting a promissory note:"
a. The Discount Date is when you sell the note to the bank.
b. The Discount Period is how long the bank holds the note until the Due Date.
c. The Proceeds is how many dollars the bank gives you on the Discount Date.
d. The Bank Discount is how many dollars the bank charges you.
e. The Bank Discount Rate is a percentage that determines the Bank Discount.
©2009 by Mark Krilanovich
This and many other handouts are available at www.silcom.com/~mkrilano
Chapter 11, page
4
Formulas to use:
1.
2.
3.
4.
5.
Interest = Face Value x Interest Rate x Time Length of Note
Maturity Value = Face Value + Interest
Discount Period = day number on Due Date - day number on Discount Date
Bank Discount = Maturity Value x Bank Discount Rate x Discount Period
Proceeds = Maturity Value - Bank Discount
Procedure to work problems:
1. Always show all your work.
2. Draw a time line.
3. Label the beginning (Date of Note), the end (Due Date) of the time line, and the
Discount Date.
4. Compute the Interest, and then the Maturity Value.
5. Compute the length of the Discount Period.
6. Compute the amount of the Bank Discount.
7. Compute the Proceeds.
8. Check: does your answer make sense?
Example Problem B:
(Bank Discount Rate = 6%; use 360 days per year)
Face Value=$4,000
Interest Rate=5%
Maturity Value
|-------------------------------------------------------------- |
90 days Length of Note
|
Due Date
|
(day 123+90=day 213)
|
August 1
|< -------------------------------------------------------- >|< ---------28 days ------>|
Date of Note
May 3 (day 123)
Discount Date (213-184=28)
July 3
(day 184)
(1) Interest = Face Value x Interest Rate x Time Length of Note
= ($4000) X (5%/year) x [(90 days)/(360 days/year)]
= $50
(2) Maturity Value = Face Value + Interest
= $4000 + $50
= $4050
(3) Discount Period = day number on Due Date - day number on Discount Date
= 213 - 184
= 28 days
(4) Bank Discount = Maturity Value x Bank Discount Rate x Discount Period
= ($4050) x (6%/year) x [(28 days)/(360 days/year)]
= $18.90
(5) Proceeds = Maturity Value - Bank Discount
= $4050 - $18.90
= $4031.10
©2009 by Mark Krilanovich
This and many other handouts are available at www.silcom.com/~mkrilano