Question

In April 2016 a pound of apples cost $1.47, while oranges cost $1.11. Four years earlier the price of apples was only $1.26 a pound and that of oranges was $.97 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.)

Answer 1

a. Future value = Present value * (1+growth rate)^time

   $1.47= $1.26 * (1+growth rate)⁴

   $1.47/ $1.26 = (1+growth rate)⁴

   1.1667 = (1+growth rate)⁴

   1.0393 = (1+growth rate)

   1.0393 -1 = growth rate)

   3.93% = growth rate

b. $1.11 = $0.97 * (1+ growth)⁴

   1.11 / 0.97 = (1+ growth)⁴

   1.1443 = (1+ growth)⁴

1.0343 =1 + growth

3.43% = growth

c. future value = Present value * (1+growth rate)^time

      = $1.47 * (1 + 0.0393) ¹⁴

= $1.47 * (1.0393)¹⁴

= $1.47 * 1.71543

= $2.52

Note:- Time = 2030 - 2016

= 14 years