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Double Time Formula
Double time is a time taken or the length of time in which any quantity becomes double in size at some particular rate. The doubletime formula can be applied to calculate many things that can expand over a period of time, for example, compound interest, consumption of goods, inflation, resource extraction, population growth, etc. This concept is also known as the 'Rule of 70' because double time can be calculated by dividing 70 by the percentage growth rate. This method will also give almost the same value as the doubletime formula. The doubletime formula also helps us to understand how quickly any investment grows.
What Is Double Time Formula?
We calculate the doubletime by the doubletime formula given below:
Double Time = \(\frac{\log 2}{\log (1+r)}\)
Where,
r = content growth rate
Solved Examples Using Double Time Formula

Example 1
Determine the time it will take to double our money if we can get a constant growth rate of 7% per annum.
Solution:
To Find: Time taken to double our money.
Given: r = 7%
Now, using the doubletime formula.
\(\text{Double Time}=\frac{\log 2}{\log (1+r)}\)
= \(\frac{\log 2}{\log (1+r)}\)
= \(\frac{\log 2}{\log (1+7\%)}\)
= \(\frac{\log 2}{\log (1+0.07)}\)
= 10.24 years
Answer: It will take 10.24 years time to double our money 
Example 2:
If bank A offers a 9% constant interest rate on a certain amount and on the same amount bank B is offering a 12% constant growth rate annually. How much time will both banks take to double the amount?
Solution:
To Find: The time taken to double the amount by both the banks.
Given:
r_{bank A} = 9%
r_{bank B} = 12%
Now, using the double time formula.
\(\text{Double Time}=\frac{\log 2}{\log (1+r)}\)
For Bank A,
\(\text {Double Time}=\frac{\log 2}{\log (1+r_{bank A})}\)
\(\text {Double Time}=\frac{\log 2}{\log (1+9\%)}\)
= \(\frac{\log 2}{\log (1+0.09)}\)
= 8.04 years.
Now for bank B,
\(\text {Double Time}=\frac{\log 2}{\log (1+r_{bank B})}\)
\(\text {Double Time}=\frac{\log 2}{\log (1+12\%)}\)
= \(\frac{\log 2}{\log (1+0.12)}\)
= 6.11 yearsAnswer: Bank A will take 8.04 years and Bank B will take 6.11 years.
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