Asked by Annie
What is the doubling time of prices which are increasing by 5 percent per year?
Answers
Answered by
Steve
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.
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.