# Double Time Formula

## Double Time Formula

The term “doubling time” refers to the amount of time needed for any quantity to double in size or value. The Double Time Formula can be used to estimate resource extraction, population growth, inflation, compound interest, consumption of commodities, the number of malignant tumours, and many other things that can grow over time. The Double Time Formula  is computed by multiplying the natural logarithm of 2 by the growth exponent, or roughly by dividing 70 by the growth rate expressed as a percentage, or 70/r. The Double Time Formula given below makes it simple to compute the double-time with the aid of a constant growth rate.

## What Is Double Time Formula?

Double Time Formula is the amount of time required for any quantity to double in size at a specific rate. Numerous factors that can increase over time can be calculated using the Double Time Formula, including compound interest, product consumption, inflation, resource extraction, population growth, etc. Because the Double Time Formula may be estimated by dividing 70 by the percentage growth rate, this idea is often referred to as the “Rule of 70.” Almost the same result will be obtained using this method as with the Double Time Formula. The Double Time Formula also enables us to comprehend the rate of growth of any investment.

Double Time Formula is the period of time during which any quantity increasing at a specific rate doubles in size or amount. When determining the time at which the value of anything will double, doubling time makes the calculations of simple interest or rate growth considerably simpler.

The amount of time it takes for a population to double when it is expanding at a steady rate is one definition of doubling time. The rate is the amount that a particular parameter changes over time (for example, the rate that X population grows is 22 specimens per year). The significance of doubling time, how to determine doubling time, and how to calculate doubling time are all covered in this lesson.

### Solved Examples Using Double Time Formula

Example 1:

Calculate how long it will take for our money to double if we can maintain a 7% annual growth rate.

Solution: Time Required: To Double Our Money.

Assumed: r = 7%

Apply the double-time formula now.

Time twice

10.24 years

The answer is that it will take 10.24 years for our money to double.

Example 2:

How many years will it take to double the amount at a 10% annual growth rate?

Solution: We will use the double time algorithm to determine the time.

Formula for Double Time: log2/log(1 + r)

Since r is 10% in this case, r=10/100 = 0.10

Double time is equal to log2(1 + 0.10).

= 7.27 years

The money will therefore double in around 7.27 years.

Example 3:

Find the growth rate at which the provided sum will double in 10 years.

Solution: The double time, which is 10 years, is supplied, and we must find r.

Applying the rule of 70 now

70/r in double time

10 = 70/r

r = 70/10

r = 7

Therefore, the annual rate is 7%.