Question

In 7 years, you will be able to buy 15 oranges for 32 dollars. In 15 years, you will be able to buy 24 oranges for 76 dollars. If we assume that the annual rate of inflation stays fixed and that the cost of oranges perfectly reflects the overall consumer price index (CPI), how much would it cost to buy 47 oranges today? Round your answer to the nearest dollar.

Answer 1

Let the annual rate of inflation be r

Cost of 15 oranges 7 years from now = $32

Cost per orange 7 years from now = $32/15 = $2.13

Cost per orange today = $2.13/(1+r)⁷

Cost of 24 oranges 15 years from now = $76

Cost per orange 15 years from now = $76/24 = $3.17

Cost per orange today = $3.17/(1+r)¹⁵

$2.13/(1+r)7 = $3.17/(1+r)¹⁵

(1+r)¹⁵/(1+r)⁷ = $3.17/$2.13

(1+r)8 = $1.49

1+r = $1.49^1/8

1+r = 1.0511

r = 1.0511 - 1 = 0.0511

Annual rate of inflation = 5.11%

Cost per orange today = $2.13/1.0511⁷ = $1.50

Cost to buy 47 oranges today = $1.50*47 oranges = $70.50 = $71