 # What is Compound Interest? ( Code 0058 )

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## What is Compound Interest? Albert Einstein once called the “magic of compounding” as the eighth wonder of the world. Such is the power and potential of this useful mathematical and financial tool that it deserves the status of being among man’s greatest inventions!

Here is a look at the underlying magic of compound interest and how you can use it for your financial planning.

## What is Compound Interest?

Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. In simple terms, compound interest can be thought of as “interest on interest”. It differs from simple interest in that simple interest calculates interest only on the original principal amount, and not on the interest earned from it.

Let us clarify this with an example. If you start off with a principal amount of Rs. 2000 with an interest rate of 10%, here is how the money will multiply using compound interest, as against simple interest, over three years.

 Compound Interest Simple Interest Starting Principal: 2000 Principal: 2000 Year 1 End Principal: 2000 Interest: Rs. 200 (i.e. 10% of 2000) Principal: 2200 Interest: Rs. 200 (i.e. 10% of 2000) Year 2 End Principal: Rs. 2200 Interest: Rs. 220 (i.e. 10% of 2200) Amount: Rs. 2420 Principal: Rs. 2200 Interest: Rs. 200 (i.e. 10% of 2000) Amount: Rs. 2400 Year 3 End Principal: Rs. 2420 Interest: Rs. 242 (i.e. 10% of 2420) Amount: Rs. 2662 Principal: Rs. 2400 Interest: Rs. 200 (i.e. 10% of 2000) Amount: Rs. 2600

As can be seen, the interest increases every year with compounding, and this being spread out over a long-term, can create a huge differential.

## Mathematical Representation

A simpler formula to calculate compound interest is:

A = P (1+ r/n)nt

Where A is the future value of the investment or loan, including the interest.

P is the principal amount i.e. the initial deposit or loan amount.

R is the annual interest rate in decimals.

n is the number of times interest is compounded per year.

t is the number of years the money is invested or borrowed.

Imp: This formula gives the future value of the principal, after compounding.

## Types of Compounding

Interest can be compounded as per different time periods, for example – daily compounding, monthly compounding, quarterly compounding or yearly compounding. Monthly compounding means that interest earned will be calculated each month and added to the principal amount each month before calculating the next month’s interest. Monthly compounding results in much more interest being generated because of the high frequency of compounding. Therefore, it is important to look out for the frequency of compounding when entering financial transactions. If you are on the payer-side (for example availing a loan), a yearly frequency is advantageous. If you are on the earner side (for example investing money) a monthly frequency is better.

As can be seen from the above example, money grows exponentially with compound interest whereas it grows only linearly with simple interest. When one is on the earning side, compound interest can help your money grow significantly, over the years. This means that the earlier you start investing in compounding financial instruments, the greater will be your returns. Therefore, it is advisable to make investments in stocks, mutual funds and other financial instruments that operate on compounding, early on.

## Where is Compound Interest Applied?

Real world compound interest applications can be positive or negative for you, depending on whether you are a borrower or an investor.

Consider investing in the following compounding instruments:

• Stocks and Mutual Funds: These are great wealth-creation opportunities for the mid-term and long-term, thanks to the magic of compounding. If invested wisely, the exponential fund growth will help tide over rises in the cost of living and inflation, proving to be a cash-positive investment. Mutual funds are divested instruments, i.e. it’s like putting your eggs in many baskets, thereby reducing the risk of failure. A good way to build wealth is to reinvest the mutual fund dividends that you get to purchase more shares in the basket of companies.
• Manage Loan Repayments Better: As a rule of thumb, a lot of interest payment can be saved by simply altering the frequency of compounding i.e. changing how frequently you make the payments. For example, making half your home loan payment twice a month, rather than making the full payment once a month will save you quite a lot of interest payment.

Use caution with:

• Credit Cards: Credit card interest is generally compounded monthly, which means that if you fail to pay your credit card overdue, the amount you need to pay in further months will rise exponentially.

Compound interest can open up a whole new world of possibilities to make your money grow! It is, however, important to understand the nuances of this financial tool to be able to make the most of it and drive wealth creation.