All about Compound Interest !

Reading Time - 3 mins

Hello Everyone,

Hope you all liked my previous blog which covered the purpose of creating this blog-post and bit of my introduction. 

Thank you everyone for giving such overwhelming response to this blog-post, which I literally didn't expected. Keep reading the blog and share with your knowns if you find it helpful. 👍

Now, based on the queries and suggestions received from my blog readers, friends and close ones, I am going to pick up a very interesting topic i.e Compound Interest.

In simple words, One can define compound interest as ब्याज Pe ब्याज. 

Why Compound interest is termed differently as ?

• most powerful force in the universe
• Dunia ka आठवां अजूबा

After reading this blog, I am sure you will be also convinced that YES, Compound Interest is THE MOST POWERFUL FORCE IN THE UNIVERSE. and I MEAN IT.

Look into these graph where it is clearly shown - how an additional 1% better every day for continuous one year can result to 37.78. These shows the POWER OF COMPOUNDING.

Now, let us understand this topic in more simple way.

Today, if we visit our bank website, we can see there are various types of investment instruments such as Fixed Deposits, Recurring Deposits which all fetch compound interest, and are compounded yearly, quarterly or even monthly. (depends on bank-2-bank). 

**FYI, majorly all Indian banks provide interest compounded quarterly. 

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So, What do you mean by compounded annually, quarterly or monthly?

It is termed as Periodic compounding, which means your interest rate will be compounded as per the period defined for it, for e.g., if it is quarterly compounding, it means that the interest will be compounded every quarter (i.e., 4 time in a year).

Let us understand it by a simple example:-

Suppose you have invested Rs. 10,000 in FD for 5 years, and bank is providing you an interest rate of 7% compounded quarterly. 

Here, bank is liable to pay you interest every quarter, interest credited will be added back to your principle amount and interest for the next quarter will be calculated on the closing balance of 1st Quarter (i.e. Principal + 1st Quarter Interest).

We will understand this in more detail below.

Fun Fact- -In Stock Market, returns are compounded every moment which we can be derived by a formula 𝑒ˣ, exponential growth which again divert us into more complexity. I will make you understand that too separately in another blog. Keep reading !! 😉

 

Now coming back to our discussion-

To get back quick, look into the graph below and recall the power of CI.

I am sorry, I am breaking the motto of this blog and moving to technical part to calculate the compound interest which involves a mathematical formula but be assured I will explain you the concept in most simple and logical way:-

Here’s the formula for Compound Interest:

Amount = P (1 + [r / n]) ^ nt

• P = the principal amount (Jo aapne shuruwat me jama kia)
• r = the annual rate of interest (byaaz dar)
• n = kitne baar aapka byaaz compund hoga ek saal me (eg. Quarterly - 4 times, Half yearly - 2 times)
• t = kitne saal aapko paisa jama rakhna hai
• ^ = to the power.

Let us understand this by an simple example,

If an amount of Rs. 5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, the value of the investment after 10 years can be calculated as follows -

P = 5000.
r = 5/100 = 0.05 (decimal).
n = 12.
t = 10.

If we plug those figures into the formula, we get the following:

A = 5000 (1 + 0.05 / 12) ^{(12 * 10)} = 8235.05.

So, the investment balance after 10 years is Rs. 8,235.05 

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I guess most of us wouldn't be knowing the Rule of 72.

What is Rule of 72?

The Rule of 72 is a quick, useful formula that is popularly used to estimate the number of years required to double the invested money at a given annual rate of return.

• $\begin{array}{l}\text{t}=\; kitne\; years\; me\; aapka\; paisa\; double\; hoga.\end{array}$
• $\begin{array}{l}r\; =\; i\end{array}$nterest rate per period, as a percentage (byaaz dar)​

The Rule of 72 could apply to anything that grows at a compounded rate, such as population, macroeconomic numbers, charges, or loans.

Now let us understand this by an example :-

Suppose, if you want to know the time required to double your Rs 10,000 invested at interest rate of 7%.

So, by using the formula, t = 72/r,

we get, t = 72/7

i.e., 10.28 years, it means it will take about 10.28 years to get Rs. 10,000 doubled at int rate of 7%.

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Here's a straight-forward example of compounding on a Rs. 1,00,000 investment that earns a guaranteed 7 per cent interest. (The example assumes annual compounding and no further additions to your savings.)

As you can see, the longer your time horizon, the more significant the impact. It's a perfect example of how slow and steady wins the race. 

 

For comparison, the above example using a simple interest calculation would result in your investment growing to Rs. 2,75,000 over 25 years (Rs. 7,000 of interest paid each year on your principal amount without reinvesting). 

 

That falls short of the Rs.2,67,743 after 25 years with compounding. 😰

Majority of Indians ignores power of compounding because they fails to understand the exponential power of this tool in terms of growth.

There is lot to know about CI. Please let me know if you want any more details/ information regarding the same.

I am signing off for today.........

Please let me know in comments on what topic you people want me to get the information around and I will make every possible effort to bring out explanation for the same in simple words.

Thanks,

Ayush Garg

FinDost - A simple way to understand money !