Question

4. In October 2020 a pound of apples cost $1.32, while oranges cost $1.59. Three years earlier the price of apples was only $1.36 a pound and that of oranges was $1.51 a pound. 
a. What was the annual compound rate of growth in the price of apples and oranges? 
b. If the same rates of growth persist in the future, what will be the price of apples and oranges in 2030?

Answer 1

SOLUTION :

s.

Let growth rate be r (in decimals). 

Current year is 2020 taken as 0.

So, 

Present price , P(0) = Price 3 years ago , P(-3) * ( 1+ r)^3 

=> r = [P(0) / P(-3)]^(1/3) - 1

For apple :

=> r = (1.32 / 1.36)^(1/3) - 1

=> r = - 0.0099 = - 0.99 %  

Growth rate for apple is = - 0.99 %  (ANSWER).

For orange :

=> r = (1.51 / 1.59)^(1/3) - 1

=> r = - 0.0171 .= - 1.71 % 

Growth rate for orange is = - 1.71 %  (ANSWER).

b.

Year 2030 = 2030 - 2020 = 10 (w.r.t. current year 2020 taken as 0)

So, at the same growth rates price in 10 years from now will be :

For apple :

P(10) = P(0) ( 1 - 0.0099)^10 = 1.32 (1 - 0.0099)^10 = 1.19 ($) approx.

Price of apple in 2030 will be = 1.19 ($) approx. (ANSWER).

For orange :

P(10) = P(0) ( 1 - 0.0171)^10 = 1.51(1 - 0.0171)^10 = 1.27 ($) approx.

Price of orange in 2030 will be = 1.27 ($) approx. (ANSWER).