Compounded Interest rates: The magic of compounding - Part I

Very often we hear this term: Compounded interest rates. What is it and how it really works?

Let’s look into details of this because this term is widely used across all kinds of investments: Banks, Fixed deposits, PPF, even stock markets and other forms of businesses. In this article, I’ll also illustrate how our investments in stocks, FD etc. are affected by compounded interest rates or returns.

Assume that you have 10,000 dollars. There is a special bank account (say of type A) that is offering you 10% interest rate compounded annually while there is another bank account that is offering you same 10% interest rate, not compounded, but simple interest rate (say of type B).

So, suppose you decide to invest 10,000 each in both these accounts and you want to remain invested for 10 years long period. Since bank account A offers you compounded interest rates, the interest earned in year 1 will add to your principle amount of 10K, and this total will become the principal for next year.

This is how your money will grow in bank account A for the next 10 years:

Year	Total	Interest	Net after Interest
1.00	10,000.00	10%	11,000.00
2.00	11,000.00	10%	12,100.00
3.00	12,100.00	10%	13,310.00
4.00	13,310.00	10%	14,641.00
5.00	14,641.00	10%	16,105.10
6.00	16,105.10	10%	17,715.61
7.00	17,715.61	10%	19,487.17
8.00	19,487.17	10%	21,435.89
9.00	21,435.89	10%	23,579.48
10.00	23,579.48	10%	25,937.42

In case of account B, the interest earned in year one will not be added to your principle amount of 10K. Instead it will be paid to you. Hence, your eligible principle for each year will remain 10K and this is how it will grow in bank account B:

Year	Total	Interest	Net after Interest	Income
1.00	10,000.00	10%	11,000.00	1,000.00
2.00	10,000.00	10%	11,000.00	1,000.00
3.00	10,000.00	10%	11,000.00	1,000.00
4.00	10,000.00	10%	11,000.00	1,000.00
5.00	10,000.00	10%	11,000.00	1,000.00
6.00	10,000.00	10%	11,000.00	1,000.00
7.00	10,000.00	10%	11,000.00	1,000.00
8.00	10,000.00	10%	11,000.00	1,000.00
9.00	10,000.00	10%	11,000.00	1,000.00
10.00	10,000.00	10%	11,000.00	1,000.00
			Total Income	10,000.00

Therefore, at the end of the 10^th year, you will get back your original principle amount of 10K and over these 10 years, you would earn 1000 Rs. each year (as interest), so your total will be 10K + 10K = 20K.

Now compare the total maturity amounts from the 2 different bank accounts A & B. Bank account A with compounded interest option gives you 25,937 $, while simple interest account B gives you only 20,000 $. Definitely, in terms of money earned, you are getting more in compounded interest option.

In terms of percentage gains, income from compounded interest bank account is 30% higher than that from simple interest. Hence, this appears to be a more attractive option.

However, nothing in this world comes for free. The 30% extra income that you are receiving from compounded interest comes at a cost. The cost is in the form of loss of freedom and access to both the principle amount and for the interest earned. For compounded interest amounts, you cannot withdraw your principle amount of 10K or any of your interest earned during the entire investment horizon of 10 years. While in case of simple interest account, your principle may be locked, but you have freedom to utilize the interest amount of 1000 each year.

When we think about long term investments, we are basically willing to forego the invested money for the entire investment horizon. If that is the case, then it’s always better to opt for compounded interest. For e.g., when you open a fixed deposit account (FD), you have the option to specify how do you want your interest to work

• Interest should be reinvested (Compounded Interest)
• Interest should be paid to you (Simple Interest)

Another example that can be quoted here is of the tax saving bonds. These bonds come with a lock in period of 3 years and pay the interest annually. So at the end of each year, you receive a check (cheque) for the interest amount you earned on your investment. Therefore, this interest amount does not add up to your principle and hence your investment in bonds becomes that of a simple interest account.

So depending upon your need, you should select the right option.

Now, let’s get into some more details, carrying forward the same discussion to stocks, mutual funds and other forms of investments. We usually hear these kinds of statements, from novice investors, business experts and guest speakers on business news channels:

“Stock Markets are giving 15% returns each year”

OR

“Stock returns have been excellent since we are seeing 20% profit in stocks each year for the last 10 years”

These statements are quite commonly heard. But what’s the truth and how does it really work?

Continue to Part II of this article