=>A Method Of Estimating How Long It Will Take (In Years) To Double Your Money Using Compound Interest At A Given Rate.
=> A Method Of Estimating At What Rate Of Compound Interest It Will Take (In A Whole Number Percentage) To Double Your Money In A Given Number Of Years.
In finance, the rule of 72, the rule of 70 and the rule of 69 are methods for estimating an investment’s doubling time. The rule number (e.g., 72) is divided by the interest percentage per period to obtain the approximate number of periods (usually years) required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.
These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference, 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible. There are a number of variations to the rules that improve accuracy. For periodic compounding, the exact doubling time for an interest rate of r per period is
where T is the number of periods required. The formula above can be used for more than calculating the doubling time. If you want to know the tripling time, for example, simply replace the constant 2 in the numerator with 3. As another example, if you want to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.
You can amaze your friends and colleagues by doing compound interest computations in your head (or on a napkin, if you require one).
For example, the amount of time that is required to double your investment at a compound interest rate of 4% would be 72/4, or 18 years, while the time required to double your investment at a rate of 8% would be 72/8, or 9 years.
As another example, the rate of compound interest required to double your money in 5 years would be 72/5, or 14.4%, while the rate of compound interest required to double your money in 10 years would be 72/10, or 7.2% per year.
It’s a very good system for quick and dirty estimates of time and compound interest. Use it, and enjoy it.
Douglas E. Castle
Labels, Tags, Keywords, Categories And Search Terms For This Article: Rule of 72, computations, investments, ROI, compound interest, doubling money, The Braintenance Blog, Douglas E. Castle, math shortcuts, financial calculations, Douglas E. Castle Blog, Rule of 69, Rule of 70, Rules of thumb, capital recovery, the Payback Method.
NOTE: THE INFORMATION CONTAINED IN THIS ARTICLE SHOULD NOT BE CONSTRUED BY THE READER AS BEING LEGAL, FINANCIAL, TAX, ACCOUNTING, ECONOMIC OR INVESTMENT ADVICE. NO OFFERING OF SECURITIES OR OTHER INVESTMENT INTERESTS OF ANY TYPE IN ANY ENTITY IS MADE HEREBY, NOR IS A SOLICITATION FOR THE PURCHASE OF SECURITIES OR OTHER INVESTMENT INTERESTS OF ANY TYPE IN ANY ENTITY MADE HEREBY. THIS ARTICLE IS INTENDED FOR GENERAL INFORMATIONAL PURPOSES ONLY AND REPRESENTS THE VIEW OF THE AUTHOR ONLY.
THIS ARTICLE IS COPYRIGHT 2014 BY DOUGLAS E. CASTLE, WITH ALL RIGHTS RESERVED. ANY REPRODUCTION, TRANSMITTAL OR DISTRIBUTION OF THIS ARTICLE, EITHER IN WHOLE OR PART, IS UNAUTHORIZED AND MAY BE UNLAWFUL, UNLESS FULL ATTRIBUTION IS GIVEN TO THE AUTHOR AND ALL IMAGES AND LINKS IN THE ARTICLE REMAIN INCLUDED AND “LIVE.”
Evaluating a business’ situation and what should be done to further its best interests requires dedicated time, objectivity, emotional detachment (those latter two are different — objectivity comes from clear vision, and a grand, experienced perspective while emotional detachment comes from not being emotionally constrained from sacrificing any sacred cows, or offending anyone), and the experience and expertise of someone who has lived through a large number of these types of situations previously.
You need a tactical and strategic specialist upon whom you can truly rely. And you are already frightened that a stranger will compromise or destroy things which you have emotionally invested in.Interestingly, this very fear and attachment are the factors that keep leaders from leading the great businesses which they’ve built in moments of either crisis or critical decision.
Your business is in dire straits. You don’t know quite when it happened but your business is hurting: cash flow is very then, both fixed and variable costs seem to be on the rise, and your regional managers no longer seem motivated beyond their biweekly paycheck. You wish that you could stop everything that you’re doing and spend a few weeks examining the business in detail, but you are 1) too busy and involved in the business process and 2) not at all objective. You lack time and objectivity — and to top it off you are too emotionally involved with the business to make the changes that might have to be made. You and your attorney conferred with me, and came to the conclusion that you needed a Turnaround Consultant, and asked if I had an interest in the engagement. I am at your offices this morning, because as good a visionary, leader and hands-on manager as you are, you lack time, objectivity and the emotional detachment necessary to be effective in doing what must be done.
It requires time, objectivity and emotional detachment to do what has to be done for a business at any critical point in its evolution: whether that is averting financial disaster; contemplating adding a new product or service; thinking about outsourcing or using virtual office services to cut your staffing requirements (and the expense which comes along with having a full-time employee — now close to 37% on average of the employee’s base salary in most corporate cases); contemplating developing a virtual export or import division; evaluating a merger opportunity with a competitor in your industry who is significantly larger than you are; evaluating combining your business with you largest supplier; thinking of recapitalizing through either a private placement of equity interests, a public offering of securities, a deal with a private equity firm; a “guaranteed” public offering of your company‘s common shares through an investment banking firm; or, signing on for a large line of credit at seemingly good terms with an overseas firm out of the Middle East which only wants a 7% equity stake in your company.
When a business is at a critical inflection point in its evolution, life cycle or critical path, the key individual cannot necessarily trust or confide in anybody except for his or her lawyer or his or her accountants — but these professionals are limited in their scope of practice and expertise. The person whom you seek is usually referred to you by your legal counsel or perhaps by your independent accounting and auditing firm — and he will have those attributes necessary to guide you past that inflection point that we spoke of earlier:
It’s at these times, whether the decision involves avoiding a disaster or acquiring another firm in order to make a giant step in your business volume and diversification (not to mention the increase) in revenue sources that I feel delighted to be needed.
Thank you for reading me, and for circulating my posts through your ever-growing social media channels.
Why does BPM matter? (ebizq.net) – They Invent New Acronyms Every Week. And When They’re Not Doing That, They’re Finding New Uses For Existing Acronyms Just To Create Confusion – I Thought That “BPM” Stood For “Beats Per Minute”. That’s Why I’m One Of Those SOBs Who Avoids Acronyms.
As part of the Action Plan in any business turnaround, or in any plan of emergence from Chapter 13, reduction and restructuring of debt will play a key role, provided that the business involved in the emergence or “rescue” effort is inherently profitable by its nature — in other words — has an otherwise viable business model which was just mishandled or mismanaged in its execution. If debt can be reduced or eliminated, that is optimal; however, the second alternative which is more palatable to most lenders involves debt restructuring.
You have two restructuring objectives in dealing with lenders or bondholders – one is to defer the payment of the principal (the “balloon”) of the debt and to try to pay it on an interest-only basis for a business recovery period; the other, which is far more popular and easier to negotiate is to restructure the debt amortization or payment schedule. This second alternative permits you, as the acting Chief BusinessRestructuring Officer, to offer your creditors an option where the debt can be paid in a self-liquidating schedule, but simply over a longer time. In fact, if the length of the loan payoff schedule is sufficiently lengthened, you may even offer the creditors a small sweetener, such as a slightly higher interest rate on the loan or bond principal amount as a risk premium for their patience. Even after doing this, your payments to retire the debt in full may still be substantially lower than they would have been at a shorter (i.e., more rapid) amortization schedule.
Let’s see how this rescheduling of amortization works, Mr. Turnaround Expert:
Firstly, we’ll assume that the remaining principal amount of debt on one of our client’s loans is $80,000,000, and that at present, the client is paying off the loan at an interest rate of 8% over a five-year amortization period, fully self-liquidating. This means that the client’s monthly debt service due on the loan is approximately $162,211.
Going further, let’s assume that the client’s Chief Restructuring/ Turnaround Officer has projected (conservatively) that the cash flow available to service the loan will be approximately $175,000. This gives us a narrow margin for error. If we calculate the debt service ratio [divide the available cash flow by the the monthly loan payment obligation], it comes out to be a very, very uncomfortable 1.07884. As a lender, I would much rather see a debt service ratio that approaches 1.50000… that would make me quite comfortable, assuming that the available cash flow projections are reasonable.
If our Chief Restructuring/Turnaround Officer is a very good negotiator, and convinces the lender to reschedule the amortization of the remaining balance over a nine-year term, with a rate of 9% (our turnaround expert has given the lender an extra 1% as a risk premium for lengthening the amortization timeline), the monthly debt payments would now be $108,343.27 — we’ve cut $53,867.73 from our monthly fixed debt payment by doing this. Our new debt service ratio (assuming the $175,000 cash flow available to service the debt is the same, as it should be) will be 1.615236 instead of 1.07884. I now have a debt service ratio which exceeds the 1.50000 standard.
Amortization gives you the opportunity to stay alive longer, but yet to generate sufficient cash flows to pay off this debt, simply by changing its associated amortization schedule. We have restructured the debt brilliantly, assuming no other changes in terms on the part of the creditor, and no additional concessions to the creditor (with the exception of the 1% risk premium) on the part of our turnaround advocate, The Chief Restructuring Officer. Note that he might have chosen to cal himself the Chief Turnaround Officer, but that is too obvious and is on the edge of being Politically Incorrect. “Restructuring” sounds more positive than “Turnaround,” which conjures up images of the grim reaper following the client company’s president around.
This has given us additional cash flow margin (for coverage of other expenses of more than $53,000 per month.
Why would the creditor (a bank, represented by the officer who approved the original loan and who is responsible for handling the relationship with the client) agree to this?
Our negotiator simply took the bank officer aside and apprised him of the following facts and conclusions, gently but firmly:
1. If the client company were to go out of business and liquidate (Chapter 7, perhaps), the proceeds left to pay the bank would be less than 50% of the remaining loan principal. That would mean a substantial loss to the bank attributable directly to the officer’s decision to extend credit;
2. The foregoing could be very injurious for the officer’s career objectives, or perhaps the ability to remain employed by the bank at all;
3. If the client company remained in business, there would be no write-down or loss relating to the loan (the principal would be paid in full), and the officer would have made a good financial and career decision. His decision to allow the rescheduling of the loan has made it possible for the client company to stay in business and pay off the loan in full. Plus, the officer can speak about how “good a deal maker he was” by adding a loan premium of 1%, increasing the bank’s yield on the loan;
4. The client company keeps its deposits, its payroll account, all of its 100 or so employees have consumer loan, credit card, car loan or lease, deposits, checking or other business with the bank, all of which will now will definitely stay intact due to the officer’s “goodwill gesture to keep the company in business and everyone employed”. Interestingly, the officer also gets a credit for funds supplied to the bank (i.e., deposits — especially to demand deposit accounts (i.e., business checking), and this client has kept an average total balance in the bank of close to $1.5 million, all of which the bank earns interest on (this is called in the banking trade “playing the float”) while the client, who receives no interest waits for funds to “clear” and the bank puts this money out on overnight interest-bearing transactions with its under-reserved or slightly illiquid brethren;
5. It becomes apparent that the Chief Restructuring Officer can make the bank officer (with his own stationery, business cards, lapel pin and pens) look like a clever, prudent potentially promotable businessperson in the eyes of the client and his superiors in the bank, whom the Chief Restructuring Officer has promised to speak with (in laudatory terms) in his behalf.
The theme is not only that amortization is like fiscal alchemy — it is also that if a focal point of a turnaround Action Plan can be addressed with everyone emerging benefited (or at least not damaged as much), it can be negotiated.
Debt restructuring is a crucial part of most turnaround operations. Now you’ve gained a better insight.