The average price of a gallon of milk in 1980 was about $1.60. By the year 2016, the average price was $2.96. Determine the rate of inflation on growth in price.
The Correct Answer and Explanation is :
To determine the rate of inflation or growth in the price of milk between 1980 and 2016, we can use the formula for calculating the annual rate of inflation (compound annual growth rate, or CAGR):
[
\text{CAGR} = \left( \frac{\text{Ending Price}}{\text{Starting Price}} \right)^{\frac{1}{n}} – 1
]
Where:
- Ending Price = $2.96 (the price in 2016)
- Starting Price = $1.60 (the price in 1980)
- n = 2016 – 1980 = 36 years (the number of years between 1980 and 2016)
Step-by-step calculation:
- Substitute the values into the CAGR formula:
[
\text{CAGR} = \left( \frac{2.96}{1.60} \right)^{\frac{1}{36}} – 1
]
- Divide the prices:
[
\frac{2.96}{1.60} = 1.85
]
- Take the 36th root (since the number of years is 36):
[
1.85^{\frac{1}{36}} \approx 1.0486
]
- Subtract 1 to find the growth rate:
[
1.0486 – 1 = 0.0486
]
- Convert this decimal into a percentage:
[
0.0486 \times 100 = 4.86\%
]
Conclusion:
The compound annual growth rate (CAGR) of the price of milk between 1980 and 2016 is approximately 4.86%. This means that, on average, the price of milk increased by about 4.86% per year during this 36-year period.
Explanation:
The calculation of CAGR helps to measure the annual rate of return or growth of an investment (or price in this case) over a period of time. In this case, the 4.86% inflation rate indicates how much the price of milk has been increasing annually on average. This method is useful because it takes into account the compounding effect, meaning the price of milk increased not just linearly, but at an accelerating rate each year, due to inflationary effects on both the product and its price dynamics over time.