Question

In October 2017 a pound of apples cost $1.60, while oranges cost $1.24. Three years earlier the price of apples was only $1.39 a pound and that of oranges was $1.10 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. 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.)

Answer 1

a) This can be solved using formula of Future value

here Present value = 1.39$ , Future value = 1.6$ , r = annual compound rate = ? , n = no of years = 3

FV = PV(1+r)^n

1.6 = 1.39(1+r)^3

1.1511 = (1+r)^3

1.1511^1/3 = 1+r

1.0480 =1+r

r = 0.0480

i.e 4.80%

Thus annual compound rate in price of apple was 4.80%

b)

his can be solved using formula of Future value

here Present value = 1.1$ , Future value = 1.24$ , r = annual compound rate = ? , n = no of years = 3

FV = PV(1+r)^n

1.24 = 1.1(1+r)^3

1.1273 = (1+r)^3

1.1273^1/3 = 1+r

1.0407=1+r

r = 0.0407

i.e 4.07%

Thus annual compound rate in price of orange was 4.07%

c)

This can be solved using formula of Future value

here Present value = 1.6$ , Future value = ? , r = annual compound rate = 4.8% , n = no of years = 13

FV = PV(1+r)^n

=1.6(1+4.8%)^13

=1.6(1+0.048)^13

=1.6(1.048)^13

=1.6(1.8399)

=2.94 $

Thus in 2030 price of apple will be $ 2.94

d)

This can be solved using formula of Future value

here Present value = 1.24$ , Future value = ? , r = annual compound rate = 4.07% , n = no of years = 13

FV = PV(1+r)^n

=1.24(1+4.07%)^13

=1.24(1+0.0407)^13

=1.24(1.0407)^13

=1.24(1.6806)

=2.08 $

Thus in 2030 price of oranges will be $ 2.08