Transcript 8.1 Simple Interest - Michels Academy

8.1 Simple Interest
Key Terms
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Principal: A sum of money that is
borrowed or invested.
Simple interest: Interest earned or paid only on the
original sum of money that was
invested or borrowed.
Interest: The money earned from an investment or
the cost of borrowing money.
Amount: The total value of an investment or loan.
The amount is given by A=P+I, where A is
the amount, P is the principal, and I is
the interest.
Easy Memory Trick
I
P R T
Principal
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Is the sum of money that is borrowed
or invested
Example #1
Kenny wants to invest
$2000. Her bank will
pay 6% of the principal
each year the money is
kept in a savings
account that earns
simple interest.
Calculate the interest earned
and the amount of the
investment at the end of
each year for three years.
Record results in a table.
YEAR
0
1
2
3
INTEREST AMOUNT
EARNED
____ $2000
How to Solve
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1ST YEAR:
Given that P = $2000
Rate = 6% or 0.06
I=RxP
I = 0.06 x $2000
I = $120
$120 + $2000 = $2120
YEAR
0
INTEREST
EARNED
($)
____
AMOUNT
($)
2000
1
120
2120
2
120
2240
3
120
2360
Interest
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Simple interest: Interest earned or
paid only on the original sum of money
that was invested or borrowed.
Example #2
Vivian invests $3240 at a simple
interest rate of 2.4% per year.
a) Calculate the interest earned each
year.
b) Calculate the amount and the total
interest earned after 20 years.
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How to Solve
a) Given:
Principal = $3240
Rate = 2.4% = 0.024
Time = 1 year
Interest = PRT
I = 3240 x 0.024 x 1
= $77.76
The total interest of an
investment of $3240 for 1 year at a
simple interest rate of 2.4% is $77.76.
Continuation of example 2…
b) Given:
Amount = P + I
Principal = $3240
A = 3240 +1555.2
= 4795.20
Rate = 2.4% = 0.024
Time = 20 years
I= PRT
=3240(0.024)(20)
= 1555.20
Continuation for part b)
Total Interest = Amount – Principal
TI = 4795.20 – 3240 = $1555.20
After 20 years, Vivian will have
$4795.20 and will have earned $1555.20
in interest.
Rate
usually given as a percentage
 Expressed as a decimal when
calculating the simple interest using
the formula I= PRT
 Sometimes seen as __ %/a, which
means __% per annum, or year
 To find rate, rearrange formula
 I= PRT ( R= I / PT)
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Example #3
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Gobin has a balance of $2845 on her
credit card. What rate of simple
interest is she being charged if she
must pay $26.19 interest for the 12 days
her payment is late?
How to Solve
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Given:
Interest= 26.19
Principal= 2845
Time= 12/365
the rate of
simple interest is
28%/a.
Rate= I/ PT
Rate= 26.19/ 2845 x 12/365
= 0.28
0.28 x 100= 28%/a
Time
The length of the period
 A key element to calculating interest
 For simple interest it’s usually annually
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Example #4
Sinthura invests $4850 at a simple
interest rate of 7.6% per year. If she
wants the money to increase to $8000,
how long will she need to invest her
money?
How to Solve
Given:
P = $4850
R = 7.6% = 0.076
A = $8000
Formula: A = P + PRT
8000 = 4850 + (4850) (0.076) x T
8000 = 4850 + 368.6 x T
3150 = 368.6 x T
T = 8.546
Continuation…
Since it is over 8 years, we have to
calculate the number of days 0.546
years is.
8.546 – 8 = 0.546
0.546 x 365 days = 199.2 days
Sinthura would have to invest her
money for 8 years and 200 days to get
$8000.
Example #5
Calculate the total amount earned at the
end of each period: 1st, 2nd, 3rd, and 15th.
 $500 at 9%/a simple interest rate
A1 = P + PRT
= 500 + (500) (0.09) (1)
= 500 + 45
= $545
The total amount of an investment
of $500 for 1 year at 9%/a simple
interest is $545, and the total interest
earned is $45.
A2 = 500 + (500) (0.09) (2)
= 500+ 90
= $590
The total amount of an investment
of $500 for 2 years at 9%/a simple
interest is $590, and the total interest
earned is $90.
A3 = 500 + (500) (0.09) (3)
= 500 + 135
= $635
The total amount of an investment
of $500 for 3 years at 9%/a simple
interest is $635, and the total interest
earned is $135.
A15 = 500 + (500) (0.09) (15)
= 500 + 675
= $1175
The total amount of an investment
of $500 for 15 years at 9%/a simple
interest is $1175, and the total interest
earned is $675.
Key ideas
Simple interest is calculated only on
the principal
 (total amount) Ta and (total interest)
TI, are linear functions ,their graphs
are straight lines
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Dollars
$ 3240 Earning 2.4%/ a
simple interest
4000
3500
3000
2500
2000
1500
1000
500
0
Total Amount
Total Interest Earned
1
2
3
Year
4
5
Need to Know
To calculate simple interest
 I= PRT
I= interest
P= principal
R= interest rate ( in decimal)
T= time( expressed in the same period as
the interest rate, usually per year)
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Total amount of money earned from an
investment and the simple interest can be
determined by this formula
 Ta= P+ PRT
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Review your worksheets in
preparation for your up-coming
Quiz