If the price of an item increases from p1 to p2 over a period of n years, the annual rate of inflation can be modeled by i = (p2/p1)^1/n
-1
In 1945, the average value of a home was $3000. In 2012 the average value was $200,000. What was the rate of inflation for a home?
Bark
so, since you have the formula and the numbers, what's the problem?
What did you get?
The rate of inflation is 0.064688?
(200000/3000)^(1/67) -1 = 0.064688
looks good to me. Though I'd probably have said that the rate of inflation was 6.47%
To find the rate of inflation for a home, we can use the formula provided:
i = (p2/p1)^(1/n) - 1
Where:
- p1 represents the initial price/value of the home (in 1945),
- p2 represents the final price/value of the home (in 2012),
- n represents the number of years between the two prices (in this case, 2012 - 1945 = 67 years),
- i represents the annual rate of inflation.
Let's plug in the given values:
p1 = $3000
p2 = $200,000
n = 67
i = ($200,000/$3000)^(1/67) - 1
Now, let's calculate it step by step using a calculator:
1. Divide $200,000 by $3,000: 200,000 ÷ 3,000 = 66.66667.
2. Take the 67th root of 66.66667: (66.66667)^(1/67) ≈ 1.048811277.
3. Subtract 1 from the result: 1.048811277 - 1 ≈ 0.048811277.
So, the rate of inflation for a home is approximately 0.0488, or 4.88%.