What is the doubling time of prices which are increasing by 5 percent per year?
To calculate the doubling time of prices that are increasing by 5 percent per year, we can use the Rule of 70. The Rule of 70 is a simplified way to estimate the time it takes for a quantity to double given a constant growth rate.
The formula to calculate the doubling time using the Rule of 70 is:
Doubling Time = 70 / Growth Rate
In this case, the growth rate is 5 percent or 0.05 as a decimal. Plugging this value into the formula:
Doubling Time = 70 / 0.05
Simplifying the equation gives us:
Doubling Time = 1400
Therefore, the doubling time of prices increasing by 5 percent per year is approximately 1400 years.
To find the doubling time, we can use the compound interest formula:
Doubling Time = (ln(2)) / (ln(1 + r))
Where:
- "ln" represents the natural logarithm
- "r" represents the growth rate per time period
In this case, the growth rate is 5 percent per year, which can be converted to a decimal as 0.05.
Using this information, we can plug the values into the formula:
Doubling Time = (ln(2)) / (ln(1 + 0.05))
Now, let's calculate it step-by-step:
Step 1: Calculate the value within the parentheses
1 + 0.05 = 1.05
Step 2: Calculate the natural logarithm of 1.05
ln(1.05) ≈ 0.04879
Step 3: Calculate the natural logarithm of 2
ln(2) ≈ 0.69315
Step 4: Divide the natural logarithm of 2 by the natural logarithm of 1.05
0.69315 / 0.04879 ≈ 14.2067
Therefore, the doubling time of prices increasing by 5 percent per year is approximately 14.2067 years.