What is the doubling time of prices which are increasing by 5 percent per year?
Well, if prices increase by 5 percent per year, it means they will double every time someone sticks their hand in their pocket and pulls out a rabbit. Just kidding! Let's calculate the doubling time for real.
To find the doubling time, we can use the rule of 70. The rule states that you divide 70 by the annual growth rate to get the doubling time. In this case, the annual growth rate is 5 percent, or 0.05.
So, 70 divided by 0.05 equals 140. Therefore, it would take approximately 140 years for prices to double with a 5 percent annual increase. By then, we might have clown robots serving your every need!
To find the doubling time, we can use the formula:
Doubling Time = 70 / Annual Growth Rate
Given that the prices are increasing by 5 percent per year, the annual growth rate would be 0.05.
Doubling Time = 70 / 0.05
Doubling Time = 1,400 years
Therefore, it would take approximately 1,400 years for the prices to double if they are increasing by 5 percent per year.
To calculate the doubling time of prices that are increasing by 5 percent per year, we need to use the concept of compound interest.
The formula to calculate the doubling time is:
Doubling Time = (log(2)) / (log(1 + r))
In this formula, "r" represents the growth rate expressed as a decimal. Since the prices are increasing by 5 percent per year, we need to convert the percentage to a decimal by dividing it by 100:
r = 5% / 100 = 0.05
Now, we can substitute the value of "r" into the formula:
Doubling Time = (log(2)) / (log(1 + 0.05))
To find the answer, we need to calculate the logarithm values using a calculator or a mathematical software. Taking the logarithm with base 10 is typically used, denoted as "log" or "log10" depending on the tool you are using.
2 = 1.05^x
ln 2 = x ln 1.05
x = ln2/ln1.05 = 14.2 years
This is in line with the "Rule of 72" which says that a rough estimate of the doubling time at n% is 72/n years.
(1+r/100)^(72/r) is very nearly 2. AT r = 8%, it's almost exact; at other values, it's quite close.