Our goal is to figure out how long it takes for some money (or something else) to double at a certain interest rate. Rule of 72. The Rule of 72 is defined as a shortcut or rule of thumb used to estimate the number of years required to double your money at a given annual rate of return, and vice versa. Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth over time. Now let’s clean up the formula a bit. The most important property of the number e is related to the slope of exponential and logarithm functions, and it's first few digits are 2.718281828. The offers that appear in this table are from partnerships from which Investopedia receives compensation. © 2003-2020 Chegg Inc. All rights reserved. t=72/R = 72/0.5 = 144 months (since R is a monthly rate the answer is in months rather than years), 144 months = 144 months / 12 months per years = 12 years. However, since (22 – 8) is 14, and (14 ÷ 3) is 4.67 ≈ 5, the adjusted rule should use 72 + 5 = 77 for the numerator. The Rule of 72 is also used to determine how long it takes for money to halve in value for a given rate of inflation.

Now that you have a basic understanding of how the Rule of 72 works, you should have no trouble answering the following questions: Question 1: John needs to double his money in seven years to reach his financial goals. If the population of a nation increases as the rate of 1% per month, it will double in 72 months, or six years. compound interest calculation.

If you pay 15% interest on your credit cards, the amount you owe will. Remember, an 8% interest rate is the most realistic simulation for the rule. The Rule of 72 could apply to anything that grows at a compounded rate, such as population, macroeconomic numbers, charges or loans. Additionally, the Rule of 72 can be applied across all kinds of durations provided the rate of return is compounded. The formula is useful for understanding the effect of compound interest. If it takes 9 years to double a $1,000 investment, then the investment will grow to$2,000 in year 9, $4,000 in year 18,$8,000 in year 27, and so on. To remove the exponent on the right-hand side of the equation, take the natural log of each side: ﻿ln(2)=n×ln(1+r)ln(2) = n \times ln(1 + r)ln(2)=n×ln(1+r)﻿. What rate of return must he earn to do this successfully?

The Rule of 72 is also useful because it demonstrates the concept that compounding can be powerful. We want to use R as an integer (3) rather than a decimal (.03), so we multiply the right hand side by 100: There’s one last step: 69.3 is nice and all, but not easily divisible. Understanding Accounting Basics (ALOE and Balance Sheets), What You Should Know About The Stock Market, Understanding the Pareto Principle (The 80/20 Rule). Simply put, since the interest portion gets accumulated in case of compound interest, it raises the principal value with each passing month and leads to higher exponential returns overall. (Do NOT press Enter after typing the answer in each cell. The calculation of a country's GDP takes into … 4% 18 b. Joshua Kennon co-authored "The Complete Idiot's Guide to Investing, 3rd Edition" and runs his own asset management firm for the affluent. | Modified duration is a formula that expresses the measurable change in the value of a security in response to a change in interest rates. Sorry 69.3, we hardly knew ye. By not withdrawing the interest every month, the investor is increasing the principal value which helps him earn more interest. Vaaler, Leslie Jane Federer; Daniel, James W. Mathematical Interest Theory (Second Edition), Washington DC: The Mathematical Association of America, 2009, page 75. How long will it take her to double her money? Getting a rough estimate of how much time it will take to double the money also helps the average Joe to compare investments. 72 / 4 = 18. Use the Rule of 72 to estimate how long it will take to double an investment at a given interest rate.

Half the fun in using this magic formula is seeing how it’s made. The rule can also estimate the annual interest rate required to double a sum of money in a specified number of years.