Rule of 144

 Four times

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Nifty Tricks with the Rule of 72, 71, 70, 69.3, 114, 144 and My Favorites, 1.5 and 1,080,000

Written by

Rob Berger

Modified date: November 11, 2020

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If you read my article, Can You Solve this Math Problem, than you know I enjoy math. Numbers have always been my friend, and I have a few to share with you today. So let’s get to it.

Rule of 72

Many of you have heard of the Rule of 72, but let’s review just in case. To estimate the time it will take to double your money, divide 72 by the expected growth rate, expressed as a percentage. For example, if you expect to earn 10% per year on a $10,000 investment, it will double to $20,000 in about 7.2 years (72 / 10).

Now here is a neat way to use the Rule of 72 to determine annual growth rate. Let’s assume that in year 1 a company earned $2 per share, and by year 8 it was earning $8 per share. What was the annual EPS growth rate? Using the Rule of 72 makes answering this question easy. First, how many times did the EPS double over the eight year period? It doubled once from $2 to $4 and a second time from $4 to $8. Doubling twice in eight years means that the EPS doubled once every four years. Using the Rule of 72, we know that to double in 4 years the EPS must have grown at an annual compound rate of 18 (72 / 4). So the company’s EPS have grown at an annual rate of 18% over the past 8 years.

By the way, you can do the same thing to determine the growth rate of your salary (if that’s your thing). And you can use the Rule of 72 to determine, at a given inflation rate, how long it will take for your money to buy half of what it can by today (depressing).

The Rules of 71, 70 and 69.3

These rules are for us math geeks. They do the same thing as the Rule of 72, but are considered more accurate depending on the interest rate and compounding period (e.g., continuous, daily, annually). The rule of 71 is the most accurate when dealing with annual compounding. And the rule of 69.3 is more accurate for continuous or daily compounding. The Rule of 70 comes in because who wants to divide an interest rate into a number like 69.3? Ok, some do, but many don’t.

The Rules of 114 and 144

The Rules of 114 and 144 take the Rule of 72 to the next level. Rule of 114 can be used to determine how long it will take an investment to triple, and the Rule of 144 will tell you how long it will take an investment to quadruple. For example, at 10% an investment will triple in about 11 years (114 / 10) and quadruple in about 14.5 years (144 /10).

There is an important implication to the Rules of 72, 114 and 144. Notice that the numbers don’t double? That is, while it takes the interest rate divided into 72 to double, the interest rate divided into 144 doesn’t triple, it quadruples! That’s the power of compounding. And what’s the moral of this story–Save early and save often.

Rule of 114

 Three times

MONEY MATTERS-7

 POWER OF COMPOUNDING

The basic formula for compounding is

FV = PV × (1+r)ⁿ

where FV = Future Value
PV = Present Value
r = annual interest rate
n = number of periods

For example if PV is 1000,

Annual interest rate is 10%

Compounding for 5 years

The Future value will be  RS.1610.50

Compare this with simple interest. 

The future value on simple interest basis is Rs.1500 only

In other words, interest earned is higher by 22.1% at end of 5 years!

Here is how Rs.100000 multiplies when compounded at 6, 8 & 10 per cent p.a over

5,10& 15 year periods.

Years/int rate       6        8        10

5 yes                  1.34    1.47   1.61

10 yrs                 1.79     2.15   2.59

15 yrs                 2.40      3.17   4.18

(Rs. in lacs)

This shows that even a small difference of 

2 per cent makes a big difference in earnings over a period!

Also longer the period of compounding higher is the total amount at the end!

So, it is clear now one should start early to sav 

and even a small difference in rate of interest increases the final savings significantly.

Keep this in mind and more important teach your children to START SAVING EARLY and REGULARLY. 

People should start saving right from the first pay check. 

Remember to save a minimum per cent of your salary. Savings should be the first expense!

I said ‘ a per cent’ . This will imply that the absolute amount of savings increase with rising salary levels. See for yourself how the compounding would make greater impact on final amount, using the above formula. 

Interesting, Isn’t it? Compound Interest is interesting!

 MONEY MATTERS-6

Rule of 72

When interest is compounded periodically, it is added to the principal for the next period and so on until maturity. Before we study about the power of compounding, let us see the Rule of 72 as a first step.

This rule is the rule of thumb to know the interest rate or the period of compounding, given one of them for DOUBLING a principal.

As per this Rule, a principal doubles approximately, when the product of interest rate and the duration (in years) is 72. This ‘72’ is constant. For example, where a deposit carries interest rate of 12 per cent, it doubles in 6 years. Similarly, a deposit doubles in 2 years when interest rate is 36 per cent; in 3 years when interest rate is 24 per cent;

in 4 years when interest rate is 18 per cent; in 5 years when interest rate is 14.4 per cent; and in 6 years when interest rate is 12 per cent.

This rule is useful to know approximately when an amount doubles at a given interest rate or to know the implied interest rate when the period in which the amount doubles is known. Test it and understand the basic of compounding. You can show yourself off as a wizard to those who’s ready new to this Rule.

We are now ready to devolve deeply into understanding the power of compounding. Wait for the next write up!

 MONEY MATTERS-5

INTERESTING INTEREST

Now you know about Savings, it is natural you would be interested in interest earned on your savings.

Interest is expressed as ‘rate per annum’ . Banks give interest on Savings deposits at 3 per cent per annum - i.e for keeping the deposit for one year, interest is paid at Rs. 3 per Rs.100.

Postal savings give a little higher rate. Fixed deposits with banks offer different interest rates depending on the duration of the deposit. The duration ranges from a few days (say a week) to 3 years generally and beyond 3 years also. Interest rates are announced periodically. Government announces the rates for Government Savings Schemes every quarter. 

Interest may be fixed or variable. Fixed rates offer same rate for entire period of deposit.Variable rates vary periodically based on the changes to the underlying bench mark rates which changes according to market rates.

Interest rates are classified as Simple interest rate or Compound interest rates.

Simple interest rate is the rate that is applied for the entire period of deposit. Where the deposit is for, say, 3 years and interest rate is 3 per cent simple payable at maturity, interest is paid at 9 

per cent for entire 3 years ( 3 x 3 ). Interest may be paid at the end of every year also.

In the case of compound interest, interest is considered every year and added to the principal (the deposit) and second year interest is applied on the increased principal. If Rs. 100 is placed as deposit, interest at 3 per cent is applied on Rs.103. It amounts to Rs.3.09 . So the principal for third year is Rs.106.09. Interest at 3 per cent on Rs.106.09 will be Rs. 3.18. The maturity amount at the end of 3 years is Rs.109.27 as against Rs.109 under simple interest method.

Generally interest is compounded every year.It is possible to compound interest every half year or every 3 months, or even every month.It can be even every day or continuous compounding o which is known as ‘perpetual’ compounding.

We will see more interesting information on compounding in next blog. Till that time, bye.

 Money Matters -4

 SAVINGS EQUATION

How to Save more? Answer lies in knowing & understanding SAVINGS EQUATION

The equation is simple:   Savings = Income -  Expenditure  —S = I - E  

Simple, but difficult to practise!  Why I choose to express it in an equation? 

Easy to remember always.  Give it a thought as often as you can, every time you spend, which is more 

often in our life, albeit daily! LOWER the Expenditure HIGHER the SAVINGS. So, Aim to lower the 

Expenditure. Avoid the avoidable, or at least postpone. Think twice. Chances are you will not spend 

on impulsive purchases and you will realise, it was a good decision. Often this is the easier part of the 

Equation. Even rich people follow it. CAUTION : you do not have to become MISERLY!

The other leg of the Equation is INCOME. You should aim to earn more. Learn new skill, Improve your 

Qualifications, Look for better opportunities. Be assertive to get recognised for your work or efforts.

EARNING YEARS are limited unless you are on your OWN business or profession! See if you can 

aspire to be your Own Master. That is active part of Income.

Know there is a PASSIVE part of Income. Income like Interest (on savings), Dividend on Investments, 

Annuities, Capital Gains ( Profit on sale of assets/ investments), Rental Income etc fall under this 

category. Of course, you need Savings or inheritance of assets for this. 

Strive to have as many streams of passive income as possible.  Then plan, set goals and work for 

increasing them. 

Knowing this is important. Expenses by nature will increase year after year, due to needs of different 

Stages of life ad it’s responsibilities.  Above all, Inflation is unavoidable. Look back on your expenses 

one, five, ten years ago under each Head of Expenses, you will realise it. Never underestimate this aspect.

Income, at least for working class, though may increase, slowly, will cease or drastically reduce over 

a period of time. THIS TRUTH WILL STARE AT YOU. Remember this. That would help to get 

a perspective of how difficult it is to achieve your savings goal. 

SIMPLE EQUATION but requires lot of efforts to practise it. If you know this at the outset, start early to 

save, save regularly, set goal and plan and execute on both sides of the Equation, you will achieve it and 

live a happy life. 

Bye until next blog.

Money Matters-3 

                                                                 DO NOT BORROW

Saving and Borrowing seldom go together! Exceptions are there which we will see later.

If you must borrow, 1. Keep it to the minimum, 2. Borrow for short periods only. 3.Borrow for 

essential needs only. 

Prefer borrowings for productive purposes rather than for unproductive ones.

Many times, it is a vicious debt trap, leading to more and more borrowings and one would never be

able  to come out of it. Credit card debt is an excellent example for this. Do you know the interest 

charged in it is the highest ever! Next comes unsecured borrowings, pawn broking. These should be 

avoided. 

It would be better to sell your asset than taking a loan from pawn broker against the asset, usually gold, 

durable assets etc. 

Assess your ability to service a debt. It is always your surplus - Earnings & Receipts less expenses and 

outgoings. 

Exceptions I referred are borrowings for Home, Vehicle, Education. In these cases, you can get 

loans at affordable rates. EMIs should be carefully chosen, ( depends on the duration of loans, longer 

the duration, lower is the EMI but total interest outgo will be high!). Theses loans are PAYE types.

PAY AS YOU EARN types. Self liquidating in nature. You either earn out of the asset or at least 

save on (recurring) expenditure which you would otherwise have to incur. So, it makes sense.

Here again, avoid having multiple loans. I have known cases where people borrow to pa EMIs, 

surest way to ge into DEBT TRAP!

Keep this in mind. Bye until next visit.