mcgraw-hill ryerson© simple interest simple interest 6 6 6 - 1 chapter 6 mcgraw-hill ryerson© i i...
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McGraw-Hill Ryerson©
Simple
Interest
Simple
Interest 66 666 - 1
Chapter
6McGraw-Hill Ryerson©
IISS imple nterest
McGraw-Hill Ryerson©
Simple
Interest
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Interest 66 666 - 2
Calculate
Learning ObjectivesLearning
ObjectivesAfter completing this chapter, you will be able to:
… interest, maturity value,
future value, and present value
in a simple interest environment
… details of the amount and timing of payments in a time
diagram
… the equivalent value on any date of a single
payment or a stream of payments, and
Present
LO-1LO-1
LO-2LO-2
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Borrower
Example: LoanExample: Loan
Lender
PartiesParties
Lends the PrincipalLends the Principal Borrower OWES (Debt) to Lender
Borrower OWES (Debt) to Lender
LO-1LO-1
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BorrowerLender
Earns (Income) from Borrower
i.e. Interest on the Principal
Earns (Income) from Borrower
i.e. Interest on the PrincipalBorrower pays
Interest to Lender
Borrower pays Interest to Lender
Rate of Interest: Simple Interest …Calculated on an ANNUAL or
per annum (pa) basis
Simple Interest …Calculated on an ANNUAL or
per annum (pa) basis
Example: LoanExample: Loan
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ExamplesExamples
Invest $1000 at 10% simple interest for one year.
Interest earned is?
Principal X Interest Rate $1000 *10% = $100
Invest $1000 at 10% simple interest for six months.
Interest earned is?
Principal X Interest Rate $1000 * 10% $50/2 =
=
=
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Invest $1000 at 10% simple interest for three months
Interest earned is?Principal X Interest Rate = $1000 X 10% $25
Invest $1000 at 10% simple interest for one month.
Interest earned is?
Principal X Interest Rate = $1000 X 10% $8.33/12 =
/4 =
ExamplesExamples
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Up to this point we have taken months to represent 1/12th of a year, i.e. each month is treated as having the same number of days!
Would it not be more accurate to calculate the interest due or payable based on the actual number of days
in each month?
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Yes, it would! In fact, interest continues
to accumulate as each day passes!
Invest $1000 at 10% simple interest for 30 days!
Interest earned is?
ExampleExample
Principal x Interest Rate = $1000 *10% * 30
Year = 365 days or 366 in a Leap YearYear = 365 days or 366 in a Leap Year
$8.22=365
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trPI
“What is the formula that can be used to calculate SI?”
Principal Interest Rate Time
Four Elements are involved …Four Elements are involved …
Interest
Formula Formula
Principal Amount (loan or
investment)
Principal Amount (loan or
investment)
Annual Rateof SI
Annual Rateof SI
Amount (paid or received)
Amount (paid or received)
Time period …expressed as a fraction or a multiple
of a year
Time period …expressed as a fraction or a multiple
of a yearI = Prt
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Calculate the Interest earned on $5000
invested at 4% for 7 months.
Formula Formula I = Prt
I = P * r * t $5000 *
.04 * 7 /12
I = $116.67I = $116.67
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“I may need to invest or need a loan for a number
of days rather than a complete
month.”
“How do I calculate the
time between the
starting date and the ending date?”
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Interest
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Formula Formula I = Prt
Calculate the Interest earned on $5000 invested
at 4.5%
for ? .
79 Days
I =$5000*.045 * 79/365
I = $48.70I = $48.70
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Formula Formula I = Prt
I =$5000*.045 * 37/365
I = $22.81I = $22.81
Calculate the Interest earned on $5000 invested
at 4.5%
for ? .
37 Days
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Formula Formula I = Prt
I =$5000* .04 * 151/365
I = $82.74I = $82.74
Calculate the Interest earned on $5000 invested
at 4.0%
for ? .
151 Days