Compound Interest

1
Chapter 9

• Compound Interest

2
Section 1

• Compound Interest

3
Factors that influence future value

• The amount of money your investment earns depends
  upon

4
Factors that influence future value

• The amount of money your investment earns depends
  upon

5
Factors that influence future value

• The amount of money your investment earns depends
  upon

6
Visual Comparison

• Simple Interest vs Compound Interest

10,000 invested at 5 over 20 years.
7
Objective 1

• Use I PRT to compute compound interest.

8
Compound Interest

• is interest computed not only on the original
  principle, but also on any previously credited
  interest.

9
Comparison using I PRT

• Invest 580 at 3 simple interest for 4 years

580 x .03 x 1 17.40 580 x .03 x 1
17.40 580 x .03 x 1 17.40 580 x .03 x 1
17.40
69.60

• Invest 580 at 3 interest compounded annually
  for 4 years

580.00 x .03 x 1 17.40 597.40 x .03 x 1
17.92 615.32 x .03 x 1 18.46 633.78 x .03 x
1 19.01
72.79
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Compute Compound Interest 1 of 2

• Find the interest and the compound amount for a
  1500 investment earning 3 interest compounded
  every 6 months for 2 years.

11
Compute Compound Interest 2 of 2

• Find the interest and the compound amount for a
  600 investment earning 2 interest compounded
  every 3 months for 1 year.

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Objective 2

• Identify interest rate per compounding period
  number of compounding periods.

13
Compounding Period

• Compounding period is simply an amount of time
  that indicates how often interest is computed on
  an investment.

Interest Compounded Compound at the end of every Number of compounding periods in one year
semiannually 6 months 2



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Examples 1 of 3

• Determine the interest rate per period and the
  number of compounding periods over the life of
  each loan.

(a) 6 compounded quarterly, 4 years
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Examples 2 of 3

• Determine the interest rate per period and the
  number of compounding periods over the life of
  each loan.

(b) 4 compounded semiannually, 5.5 years
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Examples 3 of 3

• Determine the interest rate per period and the
  number of compounding periods over the life of
  each loan.

(c) 3 compounded monthly for 8 years.
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Objective 3

• Use M P(1 i)n to compute compound interest.

18
Exponents

• Exponents are used to represent repeated
  multiplication.

Instead of 8 x 8 x 8 x 8 x 8
85

yx
xy
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The M P(1 i)n Formula

• M P(1 i)n

• P initial investment
• n total number of compounding periods
• i interest rate per compounding period

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Example 1 of 3
M P(1 i)n

• 16, p 368
• Vickie Ewing deposits her savings of 2800 in an
  account paying 6 compounded quarterly and she
  leaves it there for 9 years.
• Compound Amount ________
• Interest __________

21
Example 2 of 3
M P(1 i)n

• 19, p 369
• 25,000 to invest.
• Loan it out at 10 simple interest for 1 year.
• Invest it _at_8 compounded quarterly for a year.
• Which option would generate the most interest,
  and by how much?

22
Example 3 of 3
M P(1 i)n

• 850 to invest.
• Invest it _at_ 3 compounded daily for 2 years.
• Compound Amount ________
• Interest __________

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Objective 4

• Use a table to compute the compound amount.

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Role of the Table
M P(1 i)n
M P x (1 i)n
M P x 1.26824
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Using the Table
(1 i)n
i Interest rate per compounding period
n number of compounding periods
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Example 1 of 4
750 deposit _at_
4 compounded annually for 3 years.
Interest Rate per Compounding Period ? Number
of Compounding Periods ?
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Example 2 of 4
750 deposit _at_
6 compounded semiannually for 5 years.
Interest Rate per Compounding Period ? Number
of Compounding Periods ?
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Example 3 of 4
750 deposit _at_
6 compounded quarterly for 2 years.
Interest Rate per Compounding Period ? Number
of Compounding Periods ?
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Example 4 of 4
750 deposit _at_
12 compounded monthly for 1 year.
Interest Rate per Compounding Period ? Number
of Compounding Periods ?
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Comparing Scenarios 1 of 1

• 22, page 369
• 18,000
• Can invest at 8 compounded quarterly.
• Find compound amount after
• 3 years ________
• 9 years ________
• The additional amt. earned by going with 9 years
  instead of 3.

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Practice

• Ch 9 Section Compound Interest
• Pages 367 369
• 4, 7,13