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In April 2013 a pound of apples cost $1.42, while oranges cost $1.06. Three year

ID: 2737108 • Letter: I

Question


In April 2013 a pound of apples cost $1.42, while oranges cost $1.06. Three years earlier the price of apples was only $1.21 a pound and that of oranges was $.92 a pound. a. What was the annual compound rate of growth in the price of apples? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Compound annual growth rate % per year b. What was the annual compound rate of growth in the price of oranges? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Compound annual growth rate % per year c. If the same rates of growth persist in the future, what will be the price of apples in 2030? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price $ d. If the same rates of growth persist in the future, what will be the price of oranges in 2030? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price $

Explanation / Answer

a.

Calculate the annual compound rate of growth in the price of apples:

= (Ending value / Beginning value )(1/no.of years)-1

= ($1.42 / $1.21)(1/3)-1

= 5.48%

b.

Calculate the annual compound rate of growth in the price of oranges:

= (Ending value / Beginning value )(1/no.of years)-1

= ($1.06 / $0.92)(1/3)-1

= 4.83%

C.

Calculate the price of apples in 2030:

Year

Interest

Future Value

Begin

$1.21

1

$0.07

$1.28

2

$0.07

$1.35

3

$0.07

$1.42

4

$0.08

$1.50

5

$0.08

$1.58

6

$0.09

$1.67

7

$0.09

$1.76

8

$0.10

$1.85

9

$0.10

$1.96

10

$0.11

$2.06

11

$0.11

$2.18

12

$0.12

$2.30

13

$0.13

$2.42

14

$0.13

$2.55

15

$0.14

$2.69

16

$0.15

$2.84

17

$0.16

$3.00

Totals

$1.79

$3.00

Therefore, the price of apples in 2030 is $3.00.

d.

Calculate the price of oranges in 2030:

Year

Interest

Future Value

Begin

$0.92

1

$0.04

$0.96

2

$0.05

$1.01

3

$0.05

$1.06

4

$0.05

$1.11

5

$0.05

$1.16

6

$0.06

$1.22

7

$0.06

$1.28

8

$0.06

$1.34

9

$0.06

$1.41

10

$0.07

$1.47

11

$0.07

$1.55

12

$0.07

$1.62

13

$0.08

$1.70

14

$0.08

$1.78

15

$0.09

$1.87

16

$0.09

$1.96

17

$0.09

$2.05

Totals

$1.13

$2.05

Therefore, the price of orange in 2030 is $2.05.

Year

Interest

Future Value

Begin

$1.21

1

$0.07

$1.28

2

$0.07

$1.35

3

$0.07

$1.42

4

$0.08

$1.50

5

$0.08

$1.58

6

$0.09

$1.67

7

$0.09

$1.76

8

$0.10

$1.85

9

$0.10

$1.96

10

$0.11

$2.06

11

$0.11

$2.18

12

$0.12

$2.30

13

$0.13

$2.42

14

$0.13

$2.55

15

$0.14

$2.69

16

$0.15

$2.84

17

$0.16

$3.00

Totals

$1.79

$3.00