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the power of compound interest |One equation to rule them all

This article is about the power of compound interest. Here I will explain a literal equation and not the self-help kind. If you are familiar with basic economics or basic mathematics, you might know this equation already. I know boring, right. But I will assure you that if you keep reading further, your perspective on money and investing will change.

Any Formula included in the book, Halves the number of Buyers.

Stephen Hawking

I am willing to take a chance with that and o be honest, I have been writing these articles in the hope that someday I will be able to turn this into a book. I know, it’s very ambitious and who the fuck would buy my book. I don’t have an answer to that. However, I do have an answer to how many mathematical equations you need to remember to start investing as a beginner.

Compound interest is the 8th wonder of the world. He who understands it earns it; he who doesn’t, pays it

Albert Einstein

In this article, I want to want to help you understand the following:

Power of Compounding

Let’s get to the point. The equation I want to discuss is simple. It’s written as follows:

F=P(1+i)^n , where F= Future amount, P=Principal Invested, I= Interest rate, N= Time

Many times in school and colleges, we have worked with this equation. But how many of us understand the power of this equation. I would go as far as to say that in the investment world, this equation is equivalent to e=mc^2. Understanding the equation for compound interest will help a lot of you make better decisions on investing your money and the returns you should from that investment.

Here’s a bitter pill, if you have “studied” four years to get a business degree and are clueless about this equation, then you just wasted your money. Regardless, I will give away this knowledge for free, and like a college, you don’t have to pay me a dime or sit in a boring lecture for 2 hours.

Significance of Compound Interest Formula in Detail

When it comes to investing, there are three variables you can control. These three variables individually give you a different level of control and Let us discuss them in detail

Principal and how it affects the equation of compound interest

This is the amount of cash you have at hand. I strongly suggest that unless you can see the future and have the power of Nostradamus. Don’t be an idiot and take out a loan to invest. You can start small. But never use someone else’s money. Use the money you have regardless of how little it is.

Now, if you are just starting, there is a perfect chance that you don’t have a lot of money to invest. Or you are afraid of investing. Being fearful of spending and not having a lot of money to invest at first is actually a good thing.

Hence, You may have a higher level of control with the amount of money you can invest. I Will say it is semi-controllable given the income you generate and the amount you spend for your necessities. The more significant the amount you invest, the larger the return you will get at the end. But this does mean that investing a lot of money, early on, does expose you to a substantially high amount of risk.

Interest rate and how it affects the equation of compound interest

I will say this is the most tricky part of the equation. Rate of return is the hardest variable to control. These statements may seem counter-intuitive at first but just bear with me. Many people fall into the trap of trying to control there rate of return. That’s a very sure-fire way to race to the bottom of the pit.

To get high returns on your investments, you have to take a proportionally high amount of risk. Whenever it comes to the rate of return, a general rule of thumb is to follow this famous quote, “if Something is too good to be true, then it probably is.” Many people chase after a high rate of return(make quick money) and lose most, if not all, their money.

Various economic factors affect interest rates—more on this in a future post. There I will try my best to explain how the economic machine functions. But for now, take me at my word, when it comes to interest rates, Chasing high returns is a terrible idea. Interest rate is a variable you want to leave alone or at least not mess with a lot. On average, a fraction of “financial experts” can “predict” the market well enough to get consistent high returns. And the difference between ordinary returns and high returns comes down to only about 1-1.5 % or less.

So, ask yourself this simple question, is gaining 1.5% more, a good trade-off for losing sleep at night. Whereas, you can still get a relatively high return if you just follow basic principles of investing and all that with minimal risks. Trust me, that extra return is not worth more than your sleep.

Time and how it affects the equation of compound interest

image to represent time in the compound interest equation

Time is the only variable you can easily control. But there is an exception. Time plays a vital role in compounding your money. Time is what gives compound interest it’s power(Literally). If you are young and are interested in investment, then you just hit the jackpot. Because if you are old and are just thinking about investing, then time may not be a luxury for you. In this case, you will be better off investing in bonds or mutual funds(more on these on a future post).

To understand how great time is to this equation. There is a simple rule you can remember. It’s called the “rule of 72”. To estimate the length of time, an amount of money takes to double, simply divide it’s assumed growth(interest rate) into 72.

For, e.g., at 6%, for instance, the money will double in 12 years (72/6=12). At 7.1%, your payment will double in 10 years.

Yes, I get it. Higher the rate of return, the faster your money will double. But here’s the thing, I never argued against that. I said if you go for the high rate of return, then you will be taking on a proportionally high amount of risk .if you have a longer time horizon, then you can take some of those risks to a certain extent but I would not advise it. There is a famous proverb in the investing realm

“the best time to invest was 10 years ago and the next best time is right now”.

The early you start, the better. In that way, you can take on more risks and can afford to lose some money in the short term.

Baises that make us a bad investor

If you study the stock market, you will see that most people are drawn towards risky, volatile stocks. Why is that? The problem is human nature. Our primitive brain has not developed fast enough to get rid of the need for instant gratification. This need for instant gratification has been a cause of human obesity, Excessive consumerism, among other things. In ancient times it was crucial to our survival that we consume what we had almost immediately because someone else could steal it or worse kill us for it.

Social media and the internet are not helping the cause either. Hence we as a society have been growing more impatient by the day. The problem with investments is that if you haven’t studied it even a little bit, it is tough to go against your primitive instinct and think long term. You have to train your mind to be more patient and not fall into confirmation bias and make impulsive decisions.

Patience is like a muscle you train. It is not easy to invest your money into something and wait 20 years and maybe even more to get a handsome return. It is almost impractical for people today to think in terms of these long periods. And our impatience is precisely the reason why we are drawn to the riskiest and volatile investments. Because nobody wants to double their money after 12 years at a mere 6% return, you would instead do it in 4 years, taking a considerable risk to get an 18% yearly return, which is unsustainable.

All men’s miseries derive from not being able to sit quiet in a room alone

Blaise Pascal

Play around with the equation

I would advise you to play around with this equation. Only, this time not using a textbook by using your speculative mind. Put different values into the variables and see the future worth of your investments. Or better you can put the amount of money you want in the future and see how much you would have to invest given the amount of time you are willing to wait and the rate of return you expect over that period.

I promise you if you start having fun with this equation, your perspective on money and investing has changed. Congratulations!. And for more detailed research check out this site

https://www.thecalculatorsite.com/articles/finance/compound-interest-formula.php

Summary

  • Compound interest is quite easy to understand and apply
  • We have many biases that make us, bad investors
  • Playing around with the equation of compound interest is quite fun

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This Post Has 6 Comments

  1. Shankar

    Power of Compounding
    Let’s get to the point. The equation I want to discuss is simple. It’s written as follows:

    F=P(1+i)^n , where F= Future amount, P=Principal Invested, I= Interest rate, N= Time

    F= ? If P=100, I=12, N=50yrs

    1. RT

      It’s F=100*(1+12%)^50
      or, F= 100*(1+(12/100))^50
      or, F=100*(1+0.12)^50
      or,F=100*(1.12)^50
      or,F=28900.21
      I.e. if you invest 100 Rs right now and it compounds at the rate of 12% for the next 50 years you will receive 28900.21 excluding taxes.
      I hope this makes things clear. And thank you for the question !!

  2. Someone

    What if the amoumt gets compounded in every three months ?
    Like in banks
    Whats the new formula?

    1. RT

      That’s a great question. But here’s the trick when banks say 4% compounding semiannually. It means you get about 2% on your principal every 6 month. Yes the final return is a little higher than 4% (may be 4.05%). But it’s not a big difference.

      If you want to go into more detail then here’s the math,
      —————————————————————————————————————————–
      e.g. Say P=4000, I=9% compounded annually for t=10 years ,
      then F= 4000(1+(9/100))^10
      then, F= 9469.45
      ——————————————————————————————————————-
      Say P=4000, I=9% compounded semi annually (every 6 months, i.e 9/2=4.5%) for t=10 years ,
      then F= 4000(1+(4.5/100))^10*2 , i.e your money compounds two times a year
      F=9646.85
      Hence, with earlier compounding you get a slightly higher amount.
      ———————————————————————————————————————–
      Similarly, Answer to your question
      Say P=4000, I=9% compounded every 3 months(i.e 9/4=2.25) for t=10 years ,
      F=4000(1+(2.25/100))^10*4 i.e your money compounds 4 times a year
      F=9740.75
      ————————————————————————————————————————-
      Hope this helps !! 🙂

  3. Rabin

    Does recurring deposit account from banks get compounded? For service person like me, saving from salary and depositing it in such account seems a safe option. But after reading your article, time duration being a major part, for many banks in Nepal, the maximum duration is only 5 years. What are your views?

    1. RT

      For the recurring deposit, this formula cannot be used or will be tedious. Instead, you can use the formula
      F= A*{[(1+i)^n-1]/i}
      Where A is the recurring deposit you want to keep:
      Here A has to be constant.
      Your return will be lower compared to if you did a large principal investment but is still a good option.
      The return is pretty low when you keep the money in banks. I would say instead consolidate your cash and put it to debentures. They are safer and give good returns(10.5% annually) and use the return and put it in another one to compound your cash although it will require you to do some work. Buy debentures from Large banks and you should be fine. The only way to lose money is if the bank collapses in which case even your saving amount is at risk. Or you can use a life insurance policy. Although the return is less but will work fine if you are risk-averse.

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