Investment in any instrument, be it a fixed deposit, debt instrument (like a corporate bond), mutual funds or shares are done with an intention to gain from the investment. This gain can be loosely termed as an interest on the capital. The aim of any investor is to maximize the interest earned on her initial invested capital at the same time ensuring that the chosen scheme of investment meets the risk tolerating capacity of the user.

Let us take an example of Ananya. Ananya has Rs 1,000 with her and she would like to earn additional money by putting her Rs 1,000 to work.   She decides to invest in a fixed deposit for 5 years. After her research she has realized that Bank 1 is giving her an interest of 7.5% and Bank 2 is giving her an interest of 8%. It is but natural to choose Bank 2. So, Ananya pays a visit to Bank 2 and has a chat with the bank manager. The bank manager asks her if she would like to receive the interest as a simple interest or would she leave her money to earn a compound interest. Puzzled, Ananya prod the bank manager to describe the difference between the two. The manager further explains.

Simple Interest: Simple interest is the interest paid to you at pre-defined regular intervals of time. You are free to withdraw the money and use it as you please. Since you are planning to invest Rs 1,000 for a 5 year period at the interest rate of 8%. At the end of each year you will receive Rs. 80 as the interest amount. After 5 years you will get back your initial deposit amount of Rs 1,000 as well.

Compound interest: However, in case of compound interest, the interest of Rs 80 that was due to you, is not handed over to you, instead it is put back to work to earn more interest and at the end of 5 years you will receive your initial deposit amount of Rs 1,000 and the accumulated interest as well.

Ananya though for a while and she decided to stick with the simple interest option. “It is good to get cash at regular interval. Moreover what is the fun in investing back such a small amount” she thought. So Ananya received Rs. 80 after each year and after 5 years she got her principal (initial deposit amount) back. In all Ananya had Rs. 400 interest earned over a period of 5 year plus the principal amount of Rs. 1000. Hence Ananya is worth Rs 1400 at the end of 5 years. Now, had Ananya resisted the temptation to receive the amount and let it compound, her investment would have grown as below:

Year 1: Principal = 1,000. Interest earned = 8% of 1,000 = 80. This Rs. 80 interest gets reinvested.

Year 2: Principal = 1,000 + 80 = 1,080. Interest earned = 8% of 1,080 ~ 86. Rs. 86 gets reinvested.

Year 3: Principal = 1,080 + 86 = 1,166. Interest earned = 8% of 1,166 ~ 93. Rs. 93 gets reinvested.

Year 4: Principal = 1,166 + 93 = 1,259. Interest earned = 8% of 1,259 ~ 100. Rs. 100 gets reinvested.

Year 5: Principal = 1,259 + 100 = 1,359. Interest earned = 8% of 1,359 ~ 109. Rs. 109 gets reinvested.

Hence, at the end of 5 years, Ananya would have at her disposal Rs. 1,359 + 109 = 1468.

Compared to Rs 1,400 she received when she opted for the simple interest option, an additional gain of Rs. 68 does not seem much. Hence it seems like a good decision from Ananya to have opted for simple interest, at least she gets additional money at the end of each year. Multiple such investments would re-inforce the feeling in Ananya that compounding may not be worth the wait. Therein lies the human fallacy. Let us assume that Ananya is a very healthy soul and she stays alive for 100 years from the day she made the fixed deposit. So Ananya decides to let her money stay in the fixed deposit for 100 years. Let us see her receivables at the end of 100 years.

Scenario 1: Simple Interest: At the end of 100 years Ananya would have: Rs. 8000 + 1000 = 9,000.

Scenario 2: Compound Interest: At the end of 100 years Ananya would have: Rs. 21,99,761 !

When adjusted for inflation this may not be a big amount 100 years down the line. But then 8% compound interest is a very conservative case. The humungous difference between Scenario 1 and Scenario 2 is due to the fact that in case of compound interest she earned interest on interest.

Compound Interest Explored:

Compound interest computation is deceptively simple. But the impact is so profound that Albert Einstein is supposed to have once said, and I quote: “Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it”. The formula for compound interest is:

0001_eqn. In short 0002_eqn

If you look at the equation there are 3 parameters or variables that contribute to the final amount earned. Let us look at how each of these makes an impact. In order to fully understand the impact of each term, we will have to keep the other two parameters constant.

Parameter 1: Initial Amount Invested (or Principle):

Let us assume that Ananya is managing her finances under some constraints. She has a hard deadline that her investments have to deliver returns by 10 years. She prefers fixed deposits and hence her rate of interest is 8% for a 10 year deposit. In these circumstances what would he Ananya’s final amount earned. In this case, the only variable parameter is the “Initial Amount Invested”.

Initial Amount Invested = 10,000. Final Amount Earned = 10,000 (1+.08)^10 = 21,590

Initial Amount Invested = 50,000. Final Amount Earned = 50,000 (1+.08)^10 = 1,07,946

Initial Amount Invested = 6,00,000. Final Amount Earned = 6,00,000 (1+.08)^10 = 12,95,354

On looking at the results we notice a fact that if we want higher final amount with a moderately low interest rate in a relatively short duration of time, you will have to invest a huge amount of money. Hence, in the above scenario, a large initial amount can lead to higher final amount earned.

Parameter 2: Rate of Interest earned:

Rate of interest is a very tricky concept. If you look around at all the possible debt instruments like fixed deposits or corporate deposits, at current consumer inflation of 6.2%, banks provide a rate of interest of about 8% to 8.5%. These are the investment options that do not require financial knowledge. You go to a bank and fill the required form and deposit your money. You will keep receiving an interest of 8% and your money keeps compounding. As we saw above, at 8% interest we were able to merely double our money in 10 years. This will not cheer up Ananya.

She has read some articles that have convinced her that, based on historical information, certain funds that invest in equities can provide returns of 12%-15%. They do not guarantee this return rate as equity markets do not guarantee anything, however empirical data has convinced her that she can earn, say 13%. Hence beyond 8%, she is entering an uncharted territory. She has to go through a gamut of Mutual fund plans, compare their returns understand their risks and finally shortlist one or more of these funds.  Let us assume she has shortlisted funds and invested Rs 1,00,000. She can stay invested for 10 years and the rate of interest she expects is 13%. At the end of 10 years she will have Rs. 3,39,456.

She is disappointed. She wants Rs. 10,00,000 after 10 years and she does not have more than Rs. 1,00, 000 to invest. If she has to earn 10,00,000 in 10 years with an initial investment of Rs 1,00,000, her investment has to grow at the rate of close to 26%. So she needs to find an investment option that gives her consistence returns of 26% every year for the next 10 years to achieve that target. This would mean that she has to do a lot of research on her own or rely on an investment advisor and keep a tab on the investments for the next 10 years.

Hence, a large rate of interest can lead to higher final amount earned.

Parameter 3: Number of Years the amount stays invested (or Time):

Ananya has worked for 3 years and has saved a moderate amount of money. Let us say she has Rs. 1,00,000. She is planning her retirement which will come in another 30 years. Her investment advisor has found out an investment option that will give her a rate of return of 15% per annum. If ananya compounds her initial sum of 1,00,000 for 30 years at the rate of 15%, then at the end of 30 years (Let us say she will be 65 years old at that time) she will have Rs. 66,21,177.

But let us suppose that she can hold on for 5 more years and then she withdraws her money after 35 years then her final amount at the age of 70 will be: 1,33,17,552. So her money doubled if she held on for 5 more years. Let us stretch her some more. What if she could wait 5 more years and withdraws her money after 40 years. She would be 75 years old and she will have Rs. 2,67,86,354. It doubled again in 5 more years and 2 crores is a tidy sum considering she invested Rs 1,00,000. Her money has multiplied 267 times.

Hence a longer time horizon can lead to a higher final amount earned.

Summary of the above experiment:

If she has to achieve the same output by relying solely on the initial investment amount, she will need to arrange for a large initial amount. Not everyone is rich to start with.

If she has to achieve the same output by using a large rate of interest, she will have to find an investment opportunity that consistently gives high return. She will have to either resort to risky methods, aka day trading, short selling, Buy today sell Tomorrow BTST, Gambling, Horse racing etc OR she has to keep finding stocks that constantly deliver higher returns for 2-3 years and shift to the next one. Either of the two methods does not guarantee success and will take a toll on her mental health.

The same result can be achieved with a modest amount, which she can eke out of her salary (moderate initial capital) search for an investment opportunity that provides achievable and realistic rate of return (moderate rate of return) and sit tight for a long long time. The magic of compounding will do the work for her.

Not everyone has huge initial capital. Not everyone has the knowledge to keep finding investment options that provide higher rate of interest. However people can potentially be invested for a longer period of time. If one keeps his/her compounding machine running for a long time then the results are very impressive. There no bigger living proof of this than Berkshire Hathaway. A look at the 2014 annual letter (you can find it here) to shareholders reveals that, since the current management under Warren Buffett took over in 1963, each class A share of Berkshire Hathaway has risen in value from $19 per share to $146,186 compounding at a rate of 19.4% ! And Mr. Buffett’s personal portfolio growth can be seen in the graph here. You can also read the complete history of Warren Buffett’s past earnings here.

Getting a hang of Compound Interest:

In [1] an interesting comparison is given for the rate of interest and the number of years required to get 100x return, i.e. if your aim is make your money grow 100 times then what should be the rate of interest and how many years you will need to achieve that. The figure below shows the mapping. So, it is clear that if the user wants to grow his money 100 times in 20 years then his rate of interest (or return) should be 26% per year for the next 20 years.

0001_0003_earning_100x_returns

There is another way of looking at the same graph, by inverting the “X” and “Y” axis [1]. The figure below shows the new view. From the figure it is quite clear that as you go from investment instruments that give a return of 20% all the way up to 30% the number of years required to grow your money hundred time merely drops from 25 years to 18 years. So if you are ready to wait for 25 years and you have found an investment instrument that gives you 20% growth year after year for the next 25 years then it may be prudent to latch on to it and let your money compound and become 100 times its initial value (note that we are talking of 100 times and not just 100%).

0001_0004_earning_100x_returns

Summary:

In summary I would like to say the following: The power of compounding is NOT because of the initial amount you invest. It is predominantly because of the other two factors, i.e., rate of interest you are able to achieve and the time period you are ready to stay invested.  And, again, out of these two, it becomes tougher to achieve very high rate of interest. So, invest (and keep investing) a decent sum of money in an instrument that gives decent rate of return for a very long time (re-investing the interest or dividend or investment proceeds) and experience the eighth wonder of the world.

Note: By the way when Einstein says “He who doesn’t… pays it…” he should be referring to debt (like credit card debt). Failure to pay back the loan amount and interest will result in the interest getting added to the principal and resulting in even higher debt. So the debt keeps compounding in this case.

References:

[1] Motilal Oswal wealth Creation Study 2014

Disclaimer:

I am not a SEBI registered research analyst. The information provided above is my subjective view based on what I have read on different websites, annual reports, and quarterly reports of various companies which I assume to be accurate. The above information should not be treated as an offer/advise to purchase a specific stock/investment instrument. Since these are my subjective opinions, I could be wrong in my understanding or presentation of information. I do not claim that the above information is complete or can be relied upon as such. We cannot be held responsible for any loss or damage caused due to any inadvertent error in the above information. We will not liable for investment decisions made by readers of this article based on the above information. I am not an investment adviser. Please consult your investment adviser for all your investment needs.

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