Where:

• 𝐴 is the amount of money accumulated after n years, including interest.

• 𝑃 is the principal amount (the initial amount of money).

• 𝑟 is the annual interest rate (decimal).

• 𝑛 is the number of times that interest is compounded per year.

• 𝑡 is the time the money is invested or borrowed for, in years.

Understanding the Rule of 72

The Rule of 72 is a straightforward way to estimate the number of years required to double the value of an investment at a given annual rate of return. 

The Rule of 72 provides a good approximation, especially for interest rates between 6% and 10%. For rates outside this range, the rule might be less accurate, but it remains a useful quick reference for most practical purposes.

Applications of the Rule of 72

#1 Estimating Investment Growth: Investors can use the Rule of 72 to quickly gauge how different interest rates affect the growth of their investments. For instance, if we have multiple investment options with varying rates of return, the rule can help us compare how quickly each investment will double our money.

#2 Understanding the Impact of Inflation: The Rule of 72 can also be applied to understand the eroding effect of inflation on purchasing power. If the inflation rate is 3%, dividing 72 by 3 indicates that prices will double approximately every 24 years, highlighting the importance of investing to preserve and grow our wealth.

#3 Financial Planning and Retirement: For long-term financial planning, the Rule of 72 can help individuals set realistic investment goals and timelines. By knowing how long it takes for investments to double, we can better plan for retirement and other long-term financial objectives.

Two example scenarios as follows: