People love the idea of doubling money with their investments. Rule of 72 is helpful to know how much time it takes to double the investment value. The mathematical calculations are difficult for individuals to compute the complex data for a particular investment. This facility is given to the investors by the Rule of 72.
Rule of 72 is a phrase or a formula that solves and calculates the approximate number of years in which an investor can double their money at a certain rate of interest. It is a simple equation which assesses how much time the investment would take to double at a predetermined interest rate. It is a shortcut for investors to estimate the investment will double their money quickly.
Rule of 72 is a kind of back-of-the-envelope calculation which uses the number 72 number as a numerator & divides by the rate of interest. This formula is very popular due to ease of use. Calculators and spreadsheet programs (excel sheets) have inbuilt features to accurately calculate & assess the required time to double the invested capital. It also computes the annual rate of compounded return of an investment.
Simple Interest versus Compound Interest
The rate of interest is charged on the investment or a loan and broadly falls into two different categories:
Simple interest is calculated by multiplying the interest rate by their principal amount and the number of days that elapse between payments. It is commonly used to determine the interest on investments when the interest is not added to the principal amount.
Compound interest is calculated by the principal amount initially and the interest accumulated on a deposit. Compound interest can be referred to as Interest on Interest. It makes the invested money grow to a higher amount at a faster pace compared to simple interest, in which the calculation is only based on the principal amount.
When the interest gets accumulated, it increases the principal amount with each passing month and leads to higher returns. If an investor doesn’t withdraw the interest amount every month, in that case, the investor is increasing their principal amount that helps to earn more interest.
On the other side, in simple interest, if the investor withdraws interest amount every month and keeps the principal value consistent, it leads to lower returns.
Rule of 72 applies to the compound interest cases only, and not in the case of simple interest.
A Formula for Rule of 72:
The following formula is used for calculating the double value of an investment:
Years (Time) Required Doubling an Investment:
This rule provides an estimated time for doubling the investment. It is a fairly accurate measure of doubling time and gives more accurate result when using lower interest rates than a higher one. It is applied for the situations of compound interest. The below-stated table showing the difference between Rule 72 calculations and the actual number of years required for an investment to double their value
Assuming that an investment will earn 8 percent per year, then the formula can be solved in order to determine the number of years which will take for the investment, and growing at 8 percent per year, to double.
In this instance, 8 is equal to the interest rate, then we will put it in for r.
N = 72 / 8
N = 9
Hence, the investment amount will double in approx in the nine years.
By rearranging the formula to identify the approximate number of years required in the investment double amount can be solved as follows:
9 = 72 / r
r = 72 / 9
r = 8, Or 8 percent interest rate
Thus, the investment requires growing at 8 percent per year to double the amount in approximately 9 years.
Other applications for Rule of 72 formula can include calculating that how many years the price of given items may double (by using an inflation rate) or determine the inflation rate with the help of the number of years which you have thought that the price of an item may double.
Assuming that inflation rate will be 3% and that a car cost Rs. 20,000. How many years will the price of a car double?
N = 72 / 3
N = 24
Resulting from that, approximately 24 years will take to double the cost of the car i.e. Rs. 40,000. Note that in the formula, the market price of the item is irrelevant for solving the equation.
Again assuming that the inflation rate is unknown and it is believed that car cost will double in approx 24 years. What will be the rate of inflation?
24 = 72 / r
r = 72 / 24
r = 3, or 3 percent rate of inflation of car.
Additionally, Rule of 72 can be used across all types of durations provided but the rate of return should be compounded. If the interest rate per quarter is 4 %, then it will take-
72 / 4 = 18 quarters
Or 4.5 years required doubling the amount of principal.
Variations in the Application of Rule of 72
Rule of 72 is accurate for the interest rates that fall between the ranges of 6% to 10%. While dealing with the above range, this rule can be modified by adding or subtracting 1 number from 72 for every 3 points of the interest rate deviated from 8% threshold.
The rate of 11% annual compounding interest is 3% than 8%. Here, adding 1 (for 3 points higher than 8%) to 72 leading to use the rule of 73 for higher precision.
For 14% rate of return, it would be applied the rule of 74 i.e. adding 2 for 6 % points higher and for 5 % rate of return, it means that reducing 1 (for 3 % points lower) to lead the rule of 71.