Rule of 69

What is Rule of 69

Rule of 69 is a general rule to estimate the time that is required to make the investment to be doubled, keeping the interest rate as a continuous compounding interest rate, i.e., the interest rate is compounding every moment. It does not provide the exact time but very close to proximity without using the pure mathematical formula.

Rule of 69 Formula

Doubling Period = 69 / Interest Rate per Annum
Rule-of-69

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Source: Rule of 69 (wallstreetmojo.com)

Type of Rules

Types of rules for calculating the no. of years take to make the investment double.

  1. Rule of 72Rule Of 72Rule of 72 is an estimated approach of calculating the time required to double the invested amount at a fixed interest rate. This is determined as a ratio of 72 to the annual interest rate. read more: It is used for the simple compound rate of interest.
  2. Rule of 70: It is used when the interest rate for the financial product is of a compoundingCompoundingCompounding is a method of investing in which the income generated by an investment is reinvested, and the new principal amount is increased by the amount of income reinvested. Depending on the time period of deposit, interest is added to the principal amount.read more nature, not of continuous compounding.
  3. Rule of 69: It is used when the interest rate is given is continuous compoundingContinuous CompoundingThe continuous compounding formula depicts the interest received when constant compounding is done for an infinite number of periods. The four variables used for its computation are the principal amount, time, interest rate and the number of the compounding period.read more.

Examples of Rule of 69

Below are some of the examples of the rule of 69.

Example #1

If an amount of $1 Mn is invested at the rate of 10%, then how much time will it take to make our investment to become $2Mn

Solution:

Calculation of doubling periodCalculation Of Doubling PeriodThe doubling time formula measures the time taken by an investment to become twice its present value. Doubling Time = ln 2 / [n * ln (1 + r/n)]; where r is the rate of return and n is the number of compounding period per year.read more will be –

Rule of 69 Example 1.1

Doubling Period = 69/10

Doubling Period = 6.9 Years.

Consider the same example; if the ask was how much time it will take to become 8 Mn, then we consider simple find it as

Initial MoneyRate of IntAt the EndTime
100102006.9
2001040013.8
4001080027.6
800101,60055.2
1,600103,200110.4
Rule of 69 Example Graph

The total time will be 27.6 Years.

Example #2

If there is a security whose compounding rate of Int. is as follows, determine the time required to make if double.

Solution:

Calculation of doubling period will be –

Example 2

Benefits of Using Rule 69

The following are the benefits of the rule of 69.

Limitations of Using Rule 69

The following are the limitations of the rule of 69.

  • Difficult to explain the logic behind the number 69.
  • Rule 69 does not apply to everything. Only the security like equity, which is compounding every minute, can provide the exact value (Rule 72 can Be help in those cases)
  • If the rate is too less like 2/3 % Per annum, than the result is not very accurate. Generally, the higher rate is well captured by this formula.
  • Projects with a heavy investment need specially designed spreadsheets because a minuscule difference in time and rate of interest value can create a difference of millions.
  • Difficult to absorb the value derived because of non-transparency of value derivation.
  • This rule covers those instrument which compounds continuously like equity shares, but it ignores the dividend component which is also received by the equity holder, so overall the share did not increase by an exact multiple of 2, but the dividend amount makes the value of it.

Important Points

This has been a guide to what is Rule of 69 and its meaning. Here we discuss formula to calculate the doubling period along with its examples, benefits, and limitations. You can learn more about accounting from the following articles –

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