Download Chapter 8

Contemporary Business Mathematics
With Canadian Applications
Eighth Edition
S. A. Hummelbrunner/K. Suzanne Coombs
PowerPoint: D. Johnston
Chapter 8
Simple Interest Applications
Copyright © 2008 Pearson Education Canada
8-1
Objectives
After completing chapter eight, the student
will be able to:
• Identify and define promissory notes and
their related terms.
• Compute the maturity value of interestbearing promissory notes.
• Compute the present value of promissory
notes.
• Compute the present value of treasury bills.
(continued)
Copyright © 2008 Pearson Education Canada
8-2
Objectives
(continued)
• Compute interest and balance for demand
loans.
• Compute interest and balances for lines of
credit and credit card loans.
• Construct repayment schedules for loans
using blended payments.
Copyright © 2008 Pearson Education Canada
8-3
Promissory Note
A promissory note is a written promise by one
party to pay a certain sum of money, with or
without interest, at a specific date or on
demand, to another party.
Copyright © 2008 Pearson Education Canada
8-4
Interest-bearing
Promissory Note
Copyright © 2008 Pearson Education Canada
8-5
Terminology of Promissory
Notes
• maker - party making promise to pay
• payee - party to whom the promise to pay
is made
• face value - sum of money (principal)
specified
• rate of interest - stated as a simple annual rate
based on the face value
(continued)
Copyright © 2008 Pearson Education Canada
8-6
Terminology of Promissory
Notes (continued)
• issue date - date on which the note was
made
• term of the note - length of time before the
note matures (becomes payable)
• due date or date of maturity - date on which the
note is paid
• interest period - time period from the date of issue
to the legal due date
Copyright © 2008 Pearson Education Canada
8-7
Promissory Notes
• The amount of interest is payable together
with the face value on the legal due date.
• The maturity value is the amount payable
on the due date (face value plus interest).
Copyright © 2008 Pearson Education Canada
8-8
Legal Due Date
• Canadian law adds three days of grace to
the term of the note to obtain the legal due
date (Bills of Exchange Act, Section 41)
Copyright © 2008 Pearson Education Canada
8-9
Legal Due Date
•
•
•
•
Interest is paid for the three days of grace.
No late payment penalty.
Credit rating remains good.
Write “No Grace Days” on the note if you
decide not to include the three days of
grace.
• The legal due date allows for cases in which
repayment date falls on a statutory holiday.
Copyright © 2008 Pearson Education Canada
8-10
Maturity Value of Interestbearing Promissory Note
S = P(1 + rt)
S = Maturity value
P = Face value of note
r = Rate of interest on note
t = Interest period (number of days between
date of issue and legal due date)
Copyright © 2008 Pearson Education Canada
8-11
Finding the Maturity Value of an
Interest-bearing Promissory Note
Compute the maturity value of a 90 day note
with a face value of $1000 issued on April 21,
2005 at an interest rate of 5.5%.
P = $1000, r = 0.055, t = 90 + 3 days of grace
S=P(1+rt) = 1000((1+.055(93)) = $1014
365
Copyright © 2008 Pearson Education Canada
8-12
Present Value of Promissory Note
S
P
1  rt
P = Face value ( or present value) of note at
issue date
S = Maturity value
r = Rate of interest
t = Interest period
Copyright © 2008 Pearson Education Canada
8-13
Finding the Present Value of a
Note
A promissory note has a maturity value of
$1258.25 and bears an annual interest rate of
8%. If you include the three days of grace,
there are 93 days in the interest period. Find
the face value or present value of the note.
S
P

1  rt
1258.25
 $1233.11
 93 
1  .08 

 365 
Copyright © 2008 Pearson Education Canada
8-14
Present Value of a Promissory
Note
• The present value is the value of the note
any time before the due date.
• The present value depends on the rate
money is worth, the time between the
present date and date of maturity, and the
maturity value.
Copyright © 2008 Pearson Education Canada
8-15
Finding the Present Value of an
Interest-bearing Note
• Step 1 -- Find the maturity value of the
note using the stated interest rate.
• Step 2 -- Calculate the present value of the
note using the rate money is worth.
Copyright © 2008 Pearson Education Canada
8-16
Finding the Present Value of an
Interest-bearing Note
A sixty-day note for $10,000 bears an annual
interest rate of 10%. Compute the present
value on the date of issue if money is worth
6%. The note matures in 63 days taking the 3
days of grace into consideration.
Step 1 -- Calculate S

 63  
S  10000 1  .10 
   $10,172.60
 365  

(continued)
Copyright © 2008 Pearson Education Canada
8-17
Finding Present Value
(continued)
Step 2 --Find present value using the issue
date as the focal date. Three days of grace
have been added to the 60 days.
S
10172.60
P

 $10, 068.33
1  rt
 63 
1  .06 

 365 
Copyright © 2008 Pearson Education Canada
8-18
Canadian Treasury Bills
• Promissory notes issued by the federal
government and most provincial
governments to meet short-term financing
needs.
• Terms of 91, 182, and 364 days.
• Do not carry an interest rate.
• No days of grace.
Copyright © 2008 Pearson Education Canada
8-19
Purchasing a T-bill
• The T-bill is purchased at a discounted
price reflecting a rate of return determined
by current market conditions.
• The discounted price is determined by
finding the present value (P) of the T-bill.
• The issuing government guarantees the
payment of face value at maturity.
Copyright © 2008 Pearson Education Canada
8-20
Calculating the Purchase Price
of a T-bill
An investment dealer bought a 182-day
Canadian T-bill with a face value of $100,000
to yield an annual return of 2.33%. Find the
purchase price.
This is a present value calculation:
100000
P
 $98,851.53
 182 
1  .0233 

 365 
Copyright © 2008 Pearson Education Canada
8-21
Demand Loans
• The lender may demand payment of the
loan in full or in part at any time.
• The borrower may repay all of the loan or
any part at any time without penalty.
• Interest, based on the unpaid balance, is
usually payable monthly.
• Interest rate is not fixed.
Copyright © 2008 Pearson Education Canada
8-22
Demand Loan
A $1200 demand loan is paid off in four
monthly payments of $300 each. In addition,
interest is charged at 6% per annum or .005
per month. The interest is calculated on the
unpaid balance using the formula:
I = Prt.
The first month’s interest is
 1 
1200(.06)  12 
= $6
(continued)
Copyright © 2008 Pearson Education Canada
8-23
Paying Off a Demand Loan
(continued)
Month
Amount Owed
Interest
1
1200
6.00
2
900
4.50
3
600
3.00
4
300
1.50
Copyright © 2008 Pearson Education Canada
8-24
Declining Balance Method
• A demand loan may be paid off by a series
of partial payments.
• Each partial payment is first applied to the
accumulated interest.
• Any remainder is used to reduce the
outstanding principal.
• Interest is always calculated on the unpaid
balance.
Copyright © 2008 Pearson Education Canada
8-25
Pointers and Pitfalls
• The date on which there is a change in the
interest rate is counted as the first day at the
new interest rate.
• The date on which a partial payment is
made is counted as the first day at the new
outstanding principal balance.
Copyright © 2008 Pearson Education Canada
8-26
Blended Payments
• The periodic payment is constant.
• The payment is first applied to the
accumulated interest.
• The remainder of the payment after the
interest has been paid is used to reduce the
unpaid principal.
• The last payment may be different.
Copyright © 2008 Pearson Education Canada
8-27
Lines of Credit
• A line of credit is a pre-approved loan
agreement between a financial institution
and a borrower.
• The borrower may withdraw money, up to
an agreed maximum, at any time.
• A minimum repayment may be required
each month.
(continued)
Copyright © 2008 Pearson Education Canada
8-28
Lines of Credit
(continued)
• The borrower may repay any additional
amount at any time without further penalty.
• The interest rate can change over time.
Copyright © 2008 Pearson Education Canada
8-29
Secured Line of Credit
• Assets are promised to the lender to cover
non-payment of the loan.
• A homeowner might pledge the value of
their home equity.
• In general, the limit is higher than the limit
of an unsecured line of credit.
• The interest rate is lower than for an
unsecured line of credit.
Copyright © 2008 Pearson Education Canada
8-30
Unsecured Line of Credit
• An unsecured line of credit is a line of
credit with no assets promised to the lender
to cover non-payment of the loan.
• The limit depends on the individual’s credit
rating and past relationship with the lender.
Copyright © 2008 Pearson Education Canada
8-31
Credit Card Loans
• A credit card entitles the bearer to a
revolving line of credit with a preestablished credit limit.
• Interest rates charged on credit cards are
higher than rates charged on loans made by
financial institutions.
• A cash advance fee may apply.
• Interest on a cash advance starts on the day
money is withdrawn.
Copyright © 2008 Pearson Education Canada
8-32
Summary
• Promissory notes, treasury bills, demand
loans,and lines of credit are important
applications of simple interest.
Copyright © 2008 Pearson Education Canada
8-33