if the price of milk has quadrupled (that is, grown four times) over the past 25 years, what has been the annual rate of inflation in milk price over that time period?
(1+i)^25 = 4
take the 25th root of both sides
1+i = 4^(1/25)
1+i = 1.0570188
i = .057 or 5.7%
check: suppose milk cost $0.50 25 years ago
now it would cost
.5(1.0570188)^25
= 2.0
which is four times what it was 25 years ago
To calculate the annual rate of inflation in the price of milk over a given time period, you need to determine the percentage of increase each year.
Here's how you can do it:
1. Start by finding the overall price increase over the 25-year period. Given that the price of milk has quadrupled, it means it has increased by a factor of 4 (4 times).
2. Calculate the annual rate of inflation by taking the nth root of the overall price increase, where n is the number of years.
Let's calculate it step by step:
1. Calculate the overall price increase:
Price increase = Quadrupling factor - 1 (since we're comparing the increase to the original price)
= 4 - 1 = 3
2. Calculate the annual rate of inflation:
Annual rate of inflation = nth root of price increase
= 3^(1/25) (since there are 25 years in the period)
Using a calculator, you can find that the annual rate of inflation in the price of milk over the last 25 years is approximately 4.69%.
Therefore, the average annual rate of inflation in milk price over the past 25 years is approximately 4.69%.