Dear Maths, please grow up and solve your own problems. I am tired of solving them for you.Anonymous

Let me begin with some interesting trivia. The moment I typed the title of this post, doubt hit me – did I spell *Maths *correctly? I mean should it be spelt *Math *or *Maths*? Fortunately, “Google Baba” came to my rescue, and I found that both spellings are correct. British English prefers *Maths *with the logic that since it is an abbreviation of Mathematics which ends with an ‘s’, Math should also end with an ‘s’- hence* Maths. *The Americans have no such qualms and leave the ‘s’ out. I decided to stick to the British version.

Out of all the subjects that I studied in my school, Maths and numbers were something which I truly feared, nay, detested. I somehow endured them till High School and then quickly shifted to Biology in my Intermediate. As I have moved on in life, though, I have realized that one can’t divorce oneself from Maths or numbers, to be precise. As my interest in personal finance developed I started to look at Maths rather fondly; the abstract numbers began making sense to me, for they could be used to prognosticate and predict financial futures, rather accurately. Today, in this post, I will introduce you to some fun facts with numbers with which you can play around and yet derive tangible outcomes which will prove crucial to your future financial planning.

**Rule of 72**

Though astonishingly simple, this rule can help you tremendously in your financial planning and throws out a multitude of outputs. In its bare essence, this rule tells you **how long will it take for your money to double**, given a particular rate of interest. All you have to do is to divide thenumber 72 by the rate of interest (or rate of return – ROR). So, if the ROR is 8%, your investment will double in nine years (72/8), but if the ROR increases to 12%, investment doubles in only six years (72/12).

If you want to calculate the required corpus for your **child’s education**, the rule of 72 is at hand to do that for you. Education inflation stands at around 10-12% in India today. Catering to a worst-case scenario, and assuming 12% education inflation, the cost of education will double every six years (72/12). So, if your child is six years old today and he pursues an engineering degree after 12 years (at age 18), the cost would have quadrupled from today’s cost – two cycles of 6 years each. Hence, if an engineering degree costs Rs 20 lakh today, you need to cater for Rs 80 lakh after 12 years.

Alternatively, if you want your money to double (or multiples thereof) in a particular **time horizon as per your financial goal**, you can decide on the investment vehicle to choose. To take an example, if you need Rs 20 lakh for your child’s college education after seven years and you have a corpus of Rs 10 lakh currently, how do you go about investing it? The historical return of Government 10 years bond (bond yield) for the last five years, is about 7% (6.98% to be precise; a minimum of 5.74% and a maximum of 8.23 %) – incidentally, a 10-year Government bond is considered akin to Sensex for debt returns. At the same time, the Sensex (Sensex Total Return Index- TRI) has given a ROR of 9.2% in the last five years. Should you decide to put this corpus in bonds, you will fall well short of the required amount. However, if you put this entire amount in equity mutual fund, while it may grow your corpus to 20 lakh in the next seven-plus years, in a worst-case scenario, you are in danger of suffering capital erosion. As a prudent investor, you would do well to divide this amount between debt and equity to have a reasonable chance of achieving your financial target.

Rule of 72 will also help you to calculate the requirement of your **retirement corpus**. If you are 36 years of age today and manage your monthly expenditure in Rs 50,000, how much will be your likely expenditure when you retire after 24 years, at the age of 60 years? The Government Consumer Price Inflation (CPI) target is 4% plus/minus 2%; hence we must calculate inflation @ 6%. Thus the cost of living would double in 12 years (72/6) and quadruple in 24 years. Therefore, the required monthly amount at retirement is likely to be Rs 2 lakh for you (annual requirement Rs 24 lakh). Going by the **4% withdrawal rule** (I will write a post on this fascinating rule subsequently), the required corpus is likely to be Rs 6 crore (Rs 24 lakh* 25). Of course, I have simplified retirement planning to explain the rule of 72 here, but there are various nuances to that. Well, a series of posts on this critical topic of retirement planning will soon follow.

Rule of 72 also helps you to calculate and take actions to guard against the pernicious impact of **inflation** on your corpus. If the inflation remains at 4% (the ideal target), the purchasing power of your corpus will erode to half in 18 years (72/4). However, if inflation surges to 6% (the upper mandated band for RBI), the purchasing power will erode to half in only 12 years (72/6). See how threatening inflation numbers could be for retirees.

**Rule of 69. **This is a slight variation to the rule of 72 and tells how long will it take for an investment to double, assuming *continuously compounding interest*. In this case, 69 is divided by the ROR instead of 72. Since it is difficult to do mental math with the figure of 69, for all practical purpose, stick with the rule of 72.

**Financial Planning with the Rule of 72**

How can we plan our asset allocation and long-term investing with the rule of 72? Let’s take the example of two 25-year-old youths who begin to earn at age 24 and retire at age 60 – an investing time of 36 years. The first one, not a prudent investor, manages his investments in a manner that it gives him a ROR of 8%. The second youth, a savvy investor, manages his investments better and earns a ROR of 12%. How different will they be at age 60 when they retire? Rule of 72 tells us that the money of the first youth will double every nine years (72/8) and the of the second one every six years (72/12). Hence, the capital of the first youth gets four cycles to “double” (36 years/9 years) – so the money doubles after nine years, quadruples after 18, octuples after 27 and grows 16 times in 36 years by the time he retires.

The second youth manages to double his money every six years (72/12) and hence experiences six investing cycles so his money doubles at six years, quadruples at 12, octuples at 18, grow 16 times at 24 years, 32 times at 30 years and 64 times at 36 years by the times he retires. **To put this difference in perspective**, **if both had invested Rs 10,000 at the beginning of their investing life, it would have grown to nearly Rs 1.6 lakh for the first youth but a humongous amount of Rs 5.9 lakh for the second one. **Well, this is being about 3.68 times wealthier, a real big deal when seen in numbers. Prudent asset allocation and periodic rebalancing thus remain the key for long term wealth creation, an aspect that I have covered at length in my books.

Another application of the rule of 72 is to look at your investments in mutual funds a little differently. All equity mutual fund houses offer two kinds of schemes – Regular and Direct plans. There is no difference in both except that in a Direct plan, you are not paying an added charge to an intermediary. The TER for a Direct plan in the same mutual fund may be less by 1% or so. To take an example of one of the most popular Large Cap mutual funds – it charges TER of 2.36% for a Regular plan and 1.35% for a Direct plan. A minor difference, you would think – but wait till I tell you the pernicious impact of this 1% extra being paid as TER.

In the last five years, this fund has given returns of 16.81% in a Direct plan and 15.68% in a Regular plan – understandably so, due to higher TER of the Regular plan. A SIP of Rs 10,000 per month done in both these schemes, which continues for 30 years, would be worth Rs 8.14 crore in a Direct plan but only Rs 6.46 crore in a Regular plan. Yes, you would be poorer by nearly Rs 1.68 crore at the time of your retirement, and obviously that money would be pocketed by your mutual fund house and intermediaries. Why such a large gap in the numbers? Due to the rule of 72 – it took 4.59 years for your money to double in a Regular plan but only 4.28 years in a Direct plan. As a result, in a period of 30 years, a Regular plan saw only 6.5 investing cycles (30/4.59) whereas a Direct plan saw seven investing cycles. Of course, the past performance of this fund may or may not be repeated, but the adverse impact of an additional 1% of TER will continue. **Be wise and switch all your “Regular” mutual fund schemes to “Direct”, tomorrow itself**.

We will continue our fun journey with numbers next week as well. In the meanwhile, please look at your investments carefully to ensure that you are not losing money inadvertently.

I am eagerly looking forward to your feedback on my books, “The Millionaire Mechanic” and “Musings of a Financially Illiterate Father”.

The Millionaire Mechanic: Financial Wisdom in the Rann

**Photo cedit: race track by Kolleen Gladden on Unsplash; dice by Alex Chambers on Unsplash**

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## 4 comments

Its awasome, u did knew that maths is also involved in planning your future ahead… Commendable

Its awasome, i didn’t knew that maths is also involved in planning your future ahead… Commendable

Again an excellent article Sir, now we wait for Sunday to receive an article from you. My son who has just finished his Graduation enjoys your articles. thank you for enriching us with knowledge

Excellent article sir. Didn’t realize that one percent could make such enormous difference. Thanks for opening my eyes.