8.1%20Simple%20Interest

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8.1 Simple Interest
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Key Terms

• 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 API, where A is the
  amount, P is the principal, and I is the
  interest.

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Easy Memory Trick
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Principal

• Is the sum of money that is borrowed or invested

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Example 1
YEAR INTEREST EARNED AMOUNT
0 ____ 2000
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• 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.

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How to Solve

• 1ST YEAR
• Given that P 2000
• Rate 6 or 0.06
• I R x P
• I 0.06 x 2000
• I 120
• 120 2000 2120

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YEAR INTEREST EARNED () AMOUNT ()
0 ____ 2000
1 120 2120
2 120 2240
3 120 2360
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Interest

• Simple interest Interest earned or paid only on
  the original sum of money that was invested or
  borrowed.

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Example 2

• Vivian invests 3240 at a simple interest rate of
  2.4 per year.
• Calculate the interest earned each year.
• 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.

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Continuation of example 2

• b) Given
• Principal 3240
• Rate 2.4 0.024
• Time 20 years
• I PRT
• 3240(0.024)(20)
• 1555.20

• Amount P I
• A 3240 1555.2
• 4795.20

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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.

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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

• 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?

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How to Solve

• Given
• Interest 26.19
• Principal 2845 the rate of Time
  12/365 simple interest is 28/a.
  Rate I/ PT
• Rate 26.19/ 2845 x 12/365
• 0.28
• 0.28 x 100 28/a

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Time

• The length of the period
• A key element to calculating interest
• For simple interest its 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?

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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

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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.

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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.

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• 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

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• 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.

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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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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