Module 11 Personal Finance

Chapter 2

Personal Finance Math (Part 1)

65

2.1 – Simple Interest

When it comes to personal finance, one of the key things to learn is the math that surrounds this topic. Once you understand the math bit, the rest is just the application of it and life becomes easy after that.

In this chapter, I’ll try and explain the most basic math involved starting from simple interest. I know this is explained across multiple chapters across multiple modules in Varsity, but for the sake of completeness let me include all of it in one single chapter.

Let us run through an imaginary transaction, my guess is that this a familiar situation for most of us.

Imagine that one of your friends needs money urgently and he approaches you for it. Being a friend, you agree to help him with the money but being a capitalist at heart, you also expect your friend to pay you ‘interest’ on the cash you lend to him. I know we don’t usually ask a friend to pay us interest, but let’s just assume he is a friend whom you’d like to help, but not at the opportunity cost of your money.

The transaction details are below –

  • Amount – Rs.100,000/-
  • Tenure – 5 years
  • Interest (%) – 10

As you can see, your friend agrees to repay Rs.100,000/- over a 5 year period and also agrees to pay you an interest of 10%.

Given this, how much money will you make at the end of 5 years? Let’s do the math and find out the details.

Remember, the yearly interest is paid on the principal amount.

Principal = Rs.100,000/-

Interest = 10%

Yearly interest amount = 10% * 100,000

= Rs.10,000/-

Here is how the math looks –

Year Principal Outstanding Interest payable
01 Rs.100,000/- Rs.10,000/-
02 Rs.100,000/- Rs.10,000/-
03 Rs.100,000/- Rs.10,000/-
04 Rs.100,000/- Rs.10,000/-
05 Rs.100,000/- Rs.10,000/-
Total Interest received Rs.50,000/-

So as you can see, you can earn Rs.50,000/- in total interest from this payment. The amount you earn from the interest can also be calculated by applying a simple formula, which you may remember from your school days –

Amount = Principal * Time * Return  

Where the return is the interest percentage.

Amount = Rs.100,000 * 5 * 10%

= Rs.50,000/-

I’m sure you’d agree that this is quite straightforward and most of you would remember that this is simple interest.

In simple interest, the interest gets charged only on the outstanding principal.

Imagine a bank transaction, you deposit Rs.100,000/- in a bank’s Fixed Deposit scheme, which promises to pay you a simple interest of 10% year on year for 5 years. At the end of 5 years, you’ll earn Rs.50,000/- as interest income. The math is still the same.

Banks don’t pay simple interest, they pay compound interest. What do you think is the difference between simple interest and compound interest?

2.2 – Compound interest

Compound interest works differently compared to simple interest. If someone agrees to pay you compound interest, then it essentially means that the person or the entity is agreeing to pay you interest on the interest already earned.

Let’s figure this out with the same example discussed above. The transaction details are as follows –

  • Amount – Rs.100,000/-
  • Tenure – 5 years
  • Interest (%) – 10
  • Interest type – Compound Interest (compounded annually)

The math is as follows –

Year 1

At the end of 1st year, you are entitled to receive a 10% interest on the principal outstanding and previous interest (if any). For a moment assume you are closing this at the end of the 1st years, then you would receive the principal amount plus the interest applicable on the principal amount.

Amount = Principal + (Principal * Interest),  this can be simplified to

= Principal * (1+ interest)

Here, (1+interest) is the ‘interest’ part and the principal is obviously the principal. Applying this –

= 100,000 *(1+10%)

= 110,000

Year 2

Now assume, you want to close this in the 2nd year instead of the first, here is how much you’d get back –

Remember, you are supposed to get paid interest on the interest earned in the first year, hence –

Principal *(1+ Interest) * (1+Interest)

The green bit is the amount receivable at the end of 1st year, and the blue bit is the interest applicable for the 2nd year.

We can simplify the above equation –

= Principal *(1+ Interest)^(2)

= 100,000*(1+10%)^(2)

= 121,000

Year 3

In the 3rd year, you’d get interest on the 1st two year’s interest as well. The math –

Principal *(1+ interest) *(1+interest) *(1+interest)

The green bit is the amount receivable at the end of 2 years, and the blue bit is the interest applicable for the 3rd year.

We can simplify the above equation –

= Principal *(1+ Interest)^(3)

= 100,000*(1+10%)^(3)

= 133,100

We can generalize this –

P*(1+R)^(n), where –

  • P = Principal
  • R = Interest rate
  • N = Tenure

So, if you were to have this open for the entire 5 years, you’d receive –

= 100,000*(1+10%)^(5)

=Rs.161,051/-

Contrast the difference between the 50K received in simple interest versus the Rs.61,051/- received via compound interest.

Compound interest and compounded return work magic in finance. At the end of the day, every aspect of personal finance boils down to the compounded return. For this reason, I think it is best to spend some more time trying to understand the concept of compounding of money.

2.3 – Compounded returns

The concept of compounded return is similar to compound interest. The concept of return and interest is very similar, just like the two sides of the same coin. The interest is what you pay when you borrow money in any form and the return is what you earn when you invest your money in any asset. Therefore, if you understand interest, then it is easy to understand the return.

In this section, you will learn about how the return is measured. Based on the time horizon of your investment, the return measurement differs.

You will use the absolute method to measure the return if your investment horizon is less than a year. Otherwise, if your investment horizon is more than a year, you will use CAGR or the compounded annual growth rate, to measure returns.

I guess the difference in absolute and CAGR is best understood with an example.

Assume you invested Rs.100,000/- on 1st Jan 2019 in a financial instrument which yields you a 10% return (per year) and you withdraw this investment a year later. How much money do you make?

Quite straight forward as you can imagine –

You will make 10% of 100,000 which is Rs.10,000/-, in other words, your investment has grown by 10% on a year on year basis. This is the absolute return. This is straightforward because the time under consideration is 1 year or 365 days.

Now, what if the same investment was held for 3 years instead of 1 year, and what if instead of a simple return of 10%, the return was compounded annually at 10%? How much money would you make at the end of 3 years?

To calculate this, we simply have to apply the growth rate formula –

Amount = Principal*(1+return)^(time)

Which as you realize is the same formula used while calculating the compound interest. Applying this formula –

100,000*(1+10%)^(3)

= Rs.133,100/-

Referring to the previous section, if you were to charge compound interest, then this is the same amount of interest you receive from your friend in the 3rd year.

Continuing on the same lines, here is another question –

If you invest Rs.100,000/- and receive Rs.133,100/- after 3 years, then what is the growth rate of your investment?

To answer this question, we just need to reorganize this formula –

Amount = Principal*(1+return)^(time)

and solve for ‘return’.

By doing so, the formula reworks itself to –

Return = [(Amount/Principal)^(1/time)] – 1

Return here is the growth rate or the CAGR.

Applying this to the problem –

CAGR = [(133100/100000)^(1/3)]-1

= 10%

2.4 – The compounding effect

Apparently, Albert Einstein once described ‘compound interest’ as the 8th wonder of the world. I guess he could not describe it any better. To understand why you need to understand the compound interest in conjunction with time.

Compounding in the finance world refers to the ability of money to grow, given that the gains of year 1 get reinvested for year 2, gains of year 2 gets reinvested for year 3, so on and so forth.

For example, consider you invest Rs.100 which is expected to grow at 20% year on year (recall this is also called the CAGR or simply the growth rate). At the end of the first year, the money grows to Rs.120.

At the end of year 1, you have two options –

  • Let Rs.20 in profits remain invested along with the original principal of Rs.100 or
  • Withdraw the profits of Rs.20

You decide not to withdraw Rs.20 profit; instead, you decide to reinvest the money for the 2nd year. At the end of the 2nd year, Rs.120 grows at 20% to Rs.144. At the end of 3rd year, Rs.144 grows at 20% to Rs.173. So on and so forth.

Compare this with withdrawing Rs.20 profits every year. Had you opted to withdraw Rs.20 every year than at the end of the 3rd year the profits collected would be Rs. 60.

However, since you decided to stay invested, the profits at the end of 3 years are Rs.173/-. This is good Rs.13 or 21.7% over Rs.60 earnt because you opted to do nothing and decided to stay invested.

This is called the compounding effect.

Let us take this analysis a little further, have a look at the chart below:

The chart above shows how Rs.100 invested at 20% grows over a 10-year period.

Here is something I want you to pay attention to. If you notice, it took 4 years for the money to grow from Rs.100 to Rs.207 (about 107% return in absolute terms). However as time progressed, from the 7th year onwards the acceleration of growth increased and it took only 3 years for a similar return of 107% to be generated (from 298 to 620).

This is in fact the most interesting property of the compounding effect.  The longer you stay invested, the harder the money works for you.

This is a very crucial lesson in personal finance. Trust me when I say that your financial well-being really depends on how well you understand this.

So please do get this concept right.

In the next chapter, we will understand the other crucial concept in personal finance – Time value of money.

Key takeaways from this chapter

  • Simple interest is the interest that gets paid only on the outstanding principal
  • Compound interest is paid on both interest and the principal outstanding
  • Interest and return are like two sides of the same coin
  • Absolute return is a measure of the growth in return when your investment if for less than a year
  • Compounded annual growth rate (CAGR) is the measure of your return when your investment duration is more than a year
  • Compounding works best when you give your investments enough time to grow

65 comments

  1. jaya says:

    sir next chapter ?

  2. sushil says:

    good initiatives basics but some times we forget basics and make investment complicated.

  3. vijay butani says:

    suggest some books for good financial literacy related

  4. Santhosh says:

    Hi, do u publish all your modules as a book. Definitely its a must read book with full of learning and knowledge. I have almost read. But I would like to keep it for any time quick reference and learning. Anyways? Thank You.

  5. Ram says:

    Hey Karthik,
    What happened to the Financial Modelling module?

  6. Dilip says:

    Karthik,

    Thanks for this Personal Finance module. This chapter will be really helpful for the people who wants to understand the effect of compounding…

    i think there is a typo
    Under section 2.4 Compounding effect
    Withdraw the profits of Rs.2 —> It should be 20 instead of 2

    Thank you again 🙂

  7. Vivek Naik says:

    Simple and easy to understand.

  8. Jaydip Kathrotiya says:

    Sir,
    Your teaching skills are god level.

  9. Shiva Teja says:

    Tell me one thing , why do you guys do it for free , just curious ,( pleasse dont make it paid after reading this comment ) i just want to know the reason thats all !

  10. Zaid says:

    Hey
    It’s really helpful and easy to understand 🙂 excellent initiative.
    Wating for IOS app. (When are you launching?)

    Thanks!

  11. Ashish mourya says:

    Dear karthik,
    I recently entered in stock market (since 30 may 2019) by opening account in zerodha only because it allowed online opening.
    Then i use marketgurukul app videos as my guide and started intraday trading .
    But since market gurukul ‘s edwardji is npt available anymore. Don’t know where he went, hope he is fine.
    There are many queries in mind when We trade in share market, so i used varsity as my guide. And since last 20 days i am reading constantly your all module step by step and benifits greatly from them. Even managed to increase capital by 2%.
    I always wanted to know about personal finance and by the grace of god you started this module .
    I have a query how can i calculate my future expense on child education etc. Tried googling it but it always give link to various financial product .
    Kindly post any formula about it,
    Also if you have any blog about financial freedom kindly share it .
    Again many many praise to zerodha and you for making trading and investing safe and happy.
    ,🙏🙏

    • Karthik Rangappa says:

      I’ve met Edward a couple of times, I hope all well with him.
      I’m glad you liked the content on Varsity, Ashish. Yes, budgeting for a future financial event will be a critical component of this module. I will surely discuss this.

  12. JAYA says:

    i taken data 10 minutes time frame for 60 days in excel i got nearly 1640 cells .
    correlation bpcl vs hpcl 0.72
    but, density curve reaches to 0.000234 below or 0.99986 above near to 1
    my question was what is the differences between collecting data for 2 years and 10 minutes time frame for 60 days ?
    which one should i need follow ? sir

  13. Vikas says:

    Thanks a lot sir … I came across Zerodha Varsity when I was searching about F&O. I really loved those 3 modules and doing some paper trading in options now. You are a great teacher and thank you for putting up these awesome contents.

  14. Prashant says:

    Sir, I have been doing the SIP in the mutual funds on regular basis till I reach my goal. I would like to ask you that how should I exit from it, whether to take out all the money from that scheme at once or should I take the small amount of money on the regular basis ?

    • Karthik Rangappa says:

      It depends on your requirements, Prashant. If you don’t have an urgency to pull funds, then stay invested. If you need it over time then withdraw small amounts on a regular period of time (this will also ensure your money stays invested for a longer period). Finally, if you need funds urgently, then you have no option but to withdraw the full amount at once.

  15. Darshan says:

    Sir, could you tell me the options to get the 12% ROI mentioned in the module without risk? If not 12%, what is the highest ROI I can get in India?

    • Karthik Rangappa says:

      Darshan, the highest risk-free return in India is about 6-7%, from the bank’s fixed deposits schemes.

  16. shambu says:

    for compound interest you said..

    Principal *(1+ Interest) * (1+Interest)

    The green bit is the amount receivable at the end of 1st year, and the blue bit is the interest applicable for the 2nd year.

    We can simplify the above equation –

    = Principal *(1+ Interest)^(2)

    = 100,000*(1+10%)^(2)

    i guess ‘The green bit is the amount receivable at the end of 1st year’ as per calculations is 110,000 and not 100000. pls help ,i could be wrong!!

    • Karthik Rangappa says:

      Yes, 1.1L is the amount receivable at the end of 1st year, provided you wish to withdraw the funds.

  17. Sundeep says:

    Sir I owe a lot of my trading success to yourself and Varsity. Thanks to you I have been taking trades based on TA and Momentum. The results have been as expected if not slightly better. Thanks a lot again for that sir. I wanted to know what are the newspapers, magazines and blogs that you read to keep up with the news? Would you give us the exhaustive list of all the resources that you use? Thanks.

    • Karthik Rangappa says:

      I’m super humbled to hear that, Sundeep. I guess it all boils down to your own discipline in the end. Hope your success continues 🙂
      I occasionally read stuff on ET/Businessline. Most of the news these days if from Twitter 🙂

  18. Nithin says:

    Karthik I read an article saying that companies have pledged their shares as a result of their share price falling down a certain limit and margin calls were triggered. Can you please explain what it means? How does a company get margin calls? Thank you.

    • Karthik Rangappa says:

      Nithin, promoters of companies pledge their shares to raise funds. The companies lending them the funds will give them based on the condition that they service the loan without any defaults. However, if the promoters default, then the lenders have to right to sell the shares and make good the money. When the lenders start selling the shares in the market, the stock price falls.

  19. yogi says:

    Hi karthik i had completed my pg in finance and having intrest in the field of markets.recently i had Passed NISM modules with help of varsity.what are the some good jobs to apply.Required skills for the future .

  20. Yusuf says:

    Recently watched your video with smallcase but didn’t understood what’s the worst advice given to you sir , can you please elaborate that. Thanks.

    • Karthik Rangappa says:

      Someone asked me to invest in Suzlon, Yusuf because it is supposed to be a ‘deep value’ stock. So I jokingly said that that was one of the worst investment advise 🙂

  21. Yusuf says:

    Thanks very much for replying.

  22. CHIDAMBARAM V says:

    Hi Sir,
    You have mentioned that “Here is something I want you to pay attention to. If you notice, it took 4 years for the money to grow from Rs.100 to Rs.207 (about 107% return in absolute terms). However as time progressed, from the 7th year onwards the acceleration of growth increased and it took only 3 years for a similar return of 107% to be generated (from 298 to 620).”

    But as per my calculation, when Rs.100 is invested at 20% CAGR the obsolute return remain same for the same period throughout the term invested.Please help me to understand. Below are my calculations:

    Year Principle intereset A=P+I Obsolute return for 4 yrs [ formula used-(A-P)/P*100 ]

    1 100 20 120
    2 120 24 144
    3 144 28.8 172.8
    4 172.8 34.56 207.36 107.36
    5 207.36 41.472 248.832 107.36
    6 248.832 49.7664 298.5984 107.36
    7 298.5984 59.71968 358.31808 107.36
    8 358.31808 71.663616 429.981696 107.36
    9 429.981696 85.9963392 515.9780352 107.36
    10 515.9780352 103.195607 619.1736422 107.36

  23. CHIDAMBARAM V says:

    Hi Sir,
    towards the starting of seventh year Rs. 298.5984 is the amount present and towards the 10th year end its Rs.620. Hence absolute return is 107.36 only. same is applicable throughout the term invested, when you calculate for 4 years duration.Kindly check

  24. Thiagarajan Krishnan says:

    I think what Chidambaram was saying is that, it takes the same 4 years (not 3 as mentioned in the post) for the return to grow from 298 to 620, as it did to grow from 100 to 207.

  25. Srinidhi says:

    Hello sir. I am a newly minted CA and I am very much interested in getting into capital markets and Investment Banking, thanks to Varsity. It has been a great learning experience for me outside of academics. My question is, CA are generally not preferred by IBs and AMCs. What skills do I need to develop on my own to be a good candidate for IB? What are the core skills needed? Thanks for the great work you are doing by spreading financial literacy.

    • Karthik Rangappa says:

      Being a CA adds a huge value especially if you want to get into the asset management side. I’d suggest you look at CFA certification, I guess with both CA and CFA, you’ll be on a great track.

  26. Srinidhi says:

    Sir thanks for the reply. I’ll look into CFA programme. Can you tell me what blogs or websites you regularly use to keep yourself updated with markets and economy? It’ll be greatly useful. Thank you.

  27. Prateek Gupta says:

    Hi sir
    Only three modules are uploaded on varsity Android app
    Eagerly waiting for fundamental analysis module to get uploaded and to give the tests.

  28. Mayur says:

    Respected Sir,

    i understood compound interest very well, its a 8th wonder as a said by the albert einstein..

    but can you tell how it work for share market , compound interest means reinvesting the INTREST again, ok i got it?

    so do i have sell share of company which i bought at lower and sell at high and whatever profit i got, have to reinvest again and buy that share again annually but big investor says think long term? so can you tell WHAT EXACTLY i have REINVEST? and hoplease help me regarding this question?

    • Karthik Rangappa says:

      Mayur, in the context of the stock markets, you have to stay invested in the stocks and let the stock accumulate its capital gains. You can even buy the stock from the dividend you receive from the company.

  29. Mayur says:

    please tell me, process of reinvesting with example. I am damm confused about it from last year I didn’t get my answer from anywhere? hope you will help me… Please

  30. Mayur says:

    Sir, it means reinvesting can done only by dividends? Becoz if I stayed invested in stock it won’t be reinvesting it will grow in linear way….? Compounding means profit on profit right? I understood about dividend no issue.. About share still Little confused… Help me regarding and sorry if I bother you…

    • Karthik Rangappa says:

      No Mayur, equities is not about the dividend play, it is about capital appreciation. For example, you invest 100 in stock this year, next year it grows to 120. The year 3rd year, your base is 120 and not 100. So your money grows with a higher base. That’s how compounding works wrt equities investing.

  31. Mayur says:

    I got it. Sir
    You are the best teacher I have ever seen…

  32. Raj says:

    Hi Karthik, Namaskara.
    Let me congratulate you and appreciate your effort in educating people with financial literacy. Unfortunately in our education system such things are not taught at early stage.
    I have a very fundamental and humble question. Me being in the timeframe where I am going through”midlife crisis”. Stuck in the vicious cycle of “job-job security-salary-liabilities”. In such situations can a person like me make a living with these stocks, MFs, derivative trading etc. If yes what’s the league that I have to play with.
    Appreciate your candid and factual advice.
    Best regards
    Raj

    • Karthik Rangappa says:

      Thanks for the kind words, Raj.
      The straight forward answer is – no. Trading income cannot substitute your business or salary income unless you have a large amount of capital specifically designated for this. This also means you have ‘other’ capital to take care of your lifestyle and family requirements. Since this is a tough ask for most of us, trading and investment income can only complement our salary. Its very hard to replace a salary/business income with trading income.

  33. Aditi says:

    Is PDF for the last chapter not available?

Post a comment