Question

In October 2017 a pound of apples cost $1.46, while oranges cost $1.10. Two years earlier the price of apples was only $1.25 a pound and that of oranges was $0.96 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.) 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.) 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.) 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.) ® Answer is complete but not entirely correct. % % Compound annual growth rate of apples Compound annual growth rate of oranges Price of apples Price of oranges 3.97 X 3.46 X 2.42 X 1.71 X $ $

Answer 1

(a)

Compute the annual growth rate for apples, using the equation as shown below:

Current price = 2 year earlier price*(1 + Growth rate)^Time

            $1.46 = $1.25*(1 + Growth rate)²

Rearrange the above equation to determine the growth rate as follows:

Growth rate = ($1.46/ $1.25)^1/2 – 1

                    = 1.08074048688 – 1

                    = 8.07%

Hence, the growth rate is 8.07%.

(b)

Compute the annual growth rate for oranges, using the equation as shown below:

Current price = 2 year earlier price*(1 + Growth rate)^Time

            $1.10 = $0.96*(1 + Growth rate)²

Rearrange the above equation to determine the growth rate as follows:

Growth rate = ($1.10/ $0.96)^1/2 – 1

                    = 1.07043604822 – 1

                    = 7.04%

Hence, the growth rate is 7.04%.

(c)

Compute the price of apples in the year 2030, using the equation as shown below:

Future Price = Year 2017 price*(1 + Growth rate)^Time

                     = $1.46*(1 + 0.08074048688)¹³

                    = $4.01

Hence, the price of apples in the year 2030 are $4.01.

(d)

Compute the price of oranges in the year 2030, using the equation as shown below:

Future Price = Year 2017 price*(1 + Growth rate)^Time

                     = $1.10*(1 + 0.07043604822)¹³

                    = $2.66

Hence, the price of oranges in year 2030 are $2.66.