In April 2013 a pound of apples cost $1.44, while oranges cost $1.08. Four years
ID: 2742675 • Letter: I
Question
In April 2013 a pound of apples cost $1.44, while oranges cost $1.08. Four years earlier the price of apples was only $1.23 a pound and that of oranges was $.94 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.)
compound annual growth rate ___
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.)
compound annual growth rate_________
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.)
compound annual growth rate___
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.)
compound annual growth rate_____
Explanation / Answer
a)
Given,
Price of the apple in 2013=1.44
Price of the apple in2010=1.23
Time period (t) =4 years
Annual compound rate of growth(r)=?
Future value = PV*(1+r)^t
(1+r)^t=FV/PV
r = (fv/pv)^1/t-1
r = ((1.44/1.23)^(1/4)-1
r=(1.170732)^(0.25)-1
r = 0.0402 or 4.02%
b)
FV=1.08,PV=0.94,t=4years
Annual compound growth rate for oranges:
r = (Fv/PV)^(1/t)-1
r = (1.08/.94)^(1/4)-1
r =0.035 or 3.53%
c)
price of apples (PV)2010=1.23
Price of the apples (Fv)=?
t = 20 years
Growth rate calculated as above=4.02%
Future value = PV*(1+r)^t
=1.23*(1+4.02%)^20
=$2.71
d)
Price of the oranges (PV)= 0.94
FV=?
t = 20years
Future value = PV*(1+r)^t
=0.94(1+0.0353)^20
=$1.88