In mid-2010 a pound of apples cost $1.38, while oranges cost $1.22. Ten years ea

Question

In mid-2010 a pound of apples cost $1.38, while oranges cost $1.22. Ten years earlier the price of apples was only $.98 a pound and that of oranges was $.76 a pound. a. What was the annual compound rate of growth in the price of the two fruits? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Annual Compound rate growth for apples % Compound rate growth for oranges % -------------------------------------------------------------------------------- b. 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 of apples in 2030 $ c. What about the price of oranges? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price of oranges in 2030 $ check my workreferencesebook & resources eBook: Inflation and the Time Value of Money Worksheet Difficulty: Intermediate Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates

Explanation / Answer

Apples Price in 2000 = 0.98$ price in 2010 = 1.38$ 1.38 = 0.98(1+r)^10 (1+r)^10 = 1.408 taking log both sides 10*log(1+r) = log(1.408) log(1+r) = 0.1486 1+r = 1.0149 r = 1.49% Oranges price in 2000 = 0.76$ price in 2010 = 1.22 1.22 = 0.76(1+r)^10 solving like above we get r = 2.076% Now in 2030 price of apple = 1.32(1.0149)^20 = 1.77$ price of oranges = 1.22(1.02076)^20 = 1.84$

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