Question

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In April 2016 a pound of apples cost $1.51, while oranges cost $1.15. Three years earlier...

In April 2016 a pound of apples cost $1.51, while oranges cost $1.15. Three years earlier the price of apples was only $1.30 a pound and that of oranges was $1.01 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. What about the price of oranges? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Solutions

Expert Solution

a. Annual compound rate of growth in the price of apples = (Price today/ Price three years ago)^(1/3) - 1

Annual compound rate of growth in the price of apples = (1.51/1.30)^(1/3) - 1

Annual compound rate of growth in the price of apples = 0.05118187751

Annual compound rate of growth in the price of apples = 5.118187751%

b. Annual compound rate of growth in the price of oranges = (Price today/ Price three years ago)^(1/3) - 1

Annual compound rate of growth in the price of oranges = (1.15/1.01)^(1/3) - 1

Annual compound rate of growth in the price of oranges = 0.04422035707

Annual compound rate of growth in the price of oranges = 4.422035707%

c. There are 14 years until 2030

Price of apples in 2030 = 1.51 * (1 +  0.05118187751)^14

Price of apples in 2030 = $3.0371557043

d. Price of oranges in 2030 = 1.15*(1+0.04422035707)^14

Price of oranges in 2030 = $2.1075991644

Can you please upvote? Thank You :-)

jeff jeffy answered 1 year ago
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