Toggle top navigation
Compounding occurs when interest is paid on reinvested interest while continuing to be paid on the original principal. Compounding uses time as an ally – the longer the process, the greater the growth.
Interest can be compounded daily, monthly, annually or any other way that a lender and borrower agree. Effective annual yield quotes take compounding into account over the investment period or term.
Following is an example of 7% interest compounded once a year for three years.
Principal $100,000
Interest year 1 7,000
New principal balance $107,000
Interest year 2 7,490
New principal balance $114,490
Interest year 3 8,014
New principal balance $122,504
Effective annual yield 7.5%
The rules of 72 and 115 provide a quick way of seeing the value and speed of compounding. These are short cuts to determine how long it takes compounded money to double and triple. To calculate how long it takes money to double, divide the interest rate into 72. To see how long money triples, divide it into 115. Assuming a 7% interest rate, it will take approximately 10.3 years for the original principal to double and 16.4 years to triple.
There is also a rule of 144. This gives an approximation of how long it takes a series of equal annual payments to double. For example, $1,000 a year deposited at 7% for 20.6 years will have $20,600 double to become $41,200.
4.00% | 5.00% | 6.00% | 7.00% | 8.00% | 9.00% | 10.00% | 11.00% | 12.00% | ||
| Rule of 72 | # yrs. to double | 18.0 | 14.4 | 12.0 | 10.3 | 9.0 | 8.0 | 7.2 | 6.5 | 6 |
| Rule of 115 | # yrs. to triple | 28.8 | 23.0 | 19.2 | 16.4 | 14.4 | 12.8 | 11.5 | 10.5 | 9.6 |
| Rule of 144 | # yrs. a series of pmts. double | 36.0 | 28.8 | 24.0 | 20.6 | 18.0 | 16.0 | 14.4 | 13.1 | 12.0 |
Compounding fallacy: The rules of 72, 115 and 144 assume that the interest will be reinvested and compounded at the original rate. This is the case when you invest in a CD with the interest accumulating or a zero coupon or discounted bond. However, when you invest in a CD, bond or stock that is paying the interest or dividend annually, that payment would have to be reinvested at the original rate in order to reach the targeted goal as planned. This is unlikely for a number of reasons, one of which is that short term rates are usually lower than long term rates. When you originally invested, you received a rate for a term that is longer than the remaining term will be for the interest payments. Unless market rates have increased, or you found a different way to invest with greater returns, you are not likelyto get the same rate as the original rate of the investment. Further, taxes can be a factor in diminishing the amount that you can reinvest. However, using these rules will give you a way of estimating the final amounts and a basis of comparing one investment to another.
Contact Us
Contact Withum’s team of professionals if you have any questions or concerns.
Read More
Managing the Monkey
Share Managing the Monkey Who works for who? If you are the boss, shouldn’t you tell those working for you what to do? Many times the boss spends inordinate […]
The Partners’ Network
Supporting Smaller Accounting Practices Organized and designed by Withum partner Edward Mendlowitz, CPA, the Partners’ Network is intended to support smaller accounting practices in areas where they need help or […]
Search Withum.com
We use cookies to improve your experience and optimize user-friendliness. Read our cookie policy for more information on the cookies we use and how to delete or block them. To continue browsing our site, please click accept.AcceptPrivacy policy
As an expert in financial advisory and business consulting, I bring a wealth of knowledge and hands-on experience in various areas, including forensic and valuation services, business management, consulting, assurance and accounting, digital solutions, cybersecurity, tax services, and industry-specific expertise.
I have a deep understanding of the concepts mentioned in the provided article, which covers a range of services offered by a professional firm. Let's break down the key concepts:
-
Advisory Services:
- Business Advisory: This includes services such as dealership advisory, healthcare advisory, insurance advisory, law firm advisory, and more.
- Forensic and Valuation Services: Encompassing areas like business disputes, economic damages, forensics, investigations, white-collar criminal defense, insolvency, bankruptcy, and receivership accounting.
-
Assurance and Accounting:
- Assurance: Providing audit services, employee benefit services, and public company SEC compliance.
- Accounting: Covering accounting and other attest engagements, international financial reporting, peer review services, and revenue recognition (ASC 606).
-
Digital Solutions and Cybersecurity:
- Digital Solutions: Involving CRM and ERP consulting services, data analytics, employee experience with Microsoft Viva, process automation solutions, and other technologies.
- Cybersecurity: Addressing cybersecurity frameworks, data privacy and compliance, forensics and electronic discovery, IT managed services, incident response, and security solutions.
-
Tax Services:
- Business and Individual Tax: Covering business tax, cost segregation, global transfer pricing, international services, state and local tax, individual tax, private client services, and Withum Wealth.
-
Industries:
- Various Sectors: Including cannabis, construction, consumer products, dealership services, financial services, healthcare, hospitality, labor unions, life sciences, manufacturing, distribution, logistics, not-for-profit and education, private equity services, professional services, real estate, technology, and emerging growth, theatre, and entertainment.
-
Insights and Education:
- Educational Resources: Offering articles, blogs, case studies, guides, events, webinars, and podcasts on topics such as financial services, law firm tax, national tax policy, opportunity zones, and year-end tax planning.
-
Specific Financial Concept:
- Compounding Rules of 72, 115, and 144: Explained by Edward Mendlowitz in the Partners' Network article, these rules provide shortcuts for determining how long it takes compounded money to double and triple, as well as an approximation for how long a series of equal annual payments will double.
It's crucial to note the compounding fallacy mentioned in the article, which emphasizes the assumptions made by the rules of 72, 115, and 144 regarding the reinvestment and compounding of interest. These rules are valuable for estimation purposes and comparing investments but may not fully account for real-world factors such as varying interest rates and taxes.
If you have any specific questions or need further clarification on these topics, feel free to reach out.
