Module 11 Personal Finance

Chapter 2

Personal Finance Math (Part 1)

25

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

25 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.

Post a comment