Question

In 5 years, you will be able to buy 16 oranges for 34 dollars. In 18 years, you will be able to buy 26 oranges for 77 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 35 oranges today?

Answer 1

let the annual inflation rate = i

5 years from now , price of 1 orange , p5= $34/16 = 2.125

18 years from now , price of 1 orange = 77/26 = 2.961538462

2.125*(1+i)^(18-5) = 2.961538462

2.125*(1+i)¹³ = 2.961538462

(1+i)¹³ = 2.961538462/2.125 = 1.393665158

1+i = (1.393665158)^(1/13) = 1.025862397

i = 1.025862397 - 1 = 0.025862397

let the price of 1 orange today = p

p*(1+i)⁵ = p5 = 2.125

p = 2.125/(1.025862397)⁵ = 1.870309067

then price of 35 oranges = 35*p = 35*1.870309067 = $65.46081734 or $65.46 ( rounding off to 2 decimal places) or $65.5 ( rounding off to 1 decimal place) or $65 ( rounding off to nearest dollar value)