Compound Interest Formula: Definition and Examples

What is Compound Interest?

 Compound interest is basically interest on interest. It is the addition of interest to the principal sum of a deposit. Interest is reinvested rather than paid out.

With compound interest, investment grows faster. Compound Interest enables investors earn more on their investment. Compound Interest can be compounded on a daily or a monthly or a quarterly basis, as per the agreement. More the number of compounding higher will be the returns. So, longer the investment, higher will be the returns.

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Compound Interest Formula: Definition and Examples

How to calculate compound interest?

Formula to calculate the amount earned with compound interest is shown:

A = P (1+R/n)^nt

Where ‘P’ stands for the principal, ‘n’ stands for the number of compounding ‘t’ stands for the investment tenure and ‘r’ is rate of interest.

Compound Interest vs Simple Interest: How the final amount varies

Below mentioned are the major differences between simple and compound interest:

Simple Interest	Compound Interest
Charged only on principal	Charged on principal along with interest
Is a small portion of principal	A small percentage of principal and simple interest earned
Returns are lower	Returns are higher
Wealth growth is lower	Wealth growth will be higher
Principal remains constant	Principal increases with time
Formula; SI = (P*T*R)/100	Formula A = P(1+R/n)nt

Examples of Simple and Compound Interest

Consider the following example; You invest INR 1,00,000 in a scheme at a rate of interest of 8% for 5 years. The amount is compounded on a quarterly basis.

In case of Simple Interest:

SI = (P*T*R) / 100

P = Principal

T= Period of investment

R = Rate of interest

SI = (1,00,000*5*8)/100

SI = 40,000

Total amount = SI + Principal = 1,00,000 + 40,000 = Rs 1,40,000.

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In case of Compound Interest:

A = P (1+R/n)^nt

A = Amount at the end of 5 years.

P = Principal invested

R = rate of interest paid

N = 4(compounded for 3 months out of 12 months or 4 times a year).

T = time period of the investment= 5 years.

A = 1,00,000 (1+ 0.08/4) ^ (4*5) = INR 1,48,595.

As you notice from the above example, the returns earned through compound interest are higher than the returns earned through simple interest.

The Rule of 72

The Rule of 72 is a simple way to determine how long an investment would take to double, given a fixed annual interest rate. The rule of 72 is highly accurate when the interest rates are low. The rule of 72 divides 72 by the annual rate of return/interest, investors can get a rough idea on how long investment would take to double.

Year	Opening Balance	Interest at 5%	Closing Balance
1	Rs 10,000	Rs 500	Rs 10,500
2	Rs 10,500	Rs 525	Rs  11,025
3	Rs  11,025	Rs 551.2	Rs 11,576.2

If the interest rate is 8% on an investment of Rs 4,00,000, then as per rule of 72, the investment would double (Rs 8,00,000) in

Time (T) = 72 / x; Where x = rate of interest.

T = 72/8 = 9 years;

Therefore, an FD offering returns of 8% would double your money in 9 years. Compound interest needs longer time to get maximum benefits and hence fixed deposits have longer duration to maturity.

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Advantages of Compound Interest:

• Better returns than simple interest
• Interest earned is compounded over time
• Better management of wealth
• Rapid return on investment

Facts about compound interest that you should know

• To enjoy compound interest benefits, you need to sacrifice today to reap benefits tomorrow: Compound interest needs a longer time of investment to enjoy the maximum benefits. It’s good to start planning for future by investing in schemes based on compound interest as the returns earned are higher.

• One need not to be rich to enjoy compound interest returns: You get corresponding returns based on your investment, be it Rs 100 or Rs 10 Lakhs.
• Compound interest can free you from credit cards: Consider interest rate is at 14% and you add just Rs 5 per month to your account. In 10 years, you'll avoid Rs 1,315 in payments.
• Compound interest is a multi-edged sword. It's good if you are saving money regularly. It can work against you if have borrowed money and have to pay compound interest.
• Compounding can be done as often as possible: More the number of compounding, more the returns earned. It’s good to compound on quarterly basis instead of annual basis. Opposite is true if you have borrowed.
• Don't be discouraged by low interest rates: Banks aren't offering high interest rate on savings accounts. Compound interest is there to take care of your returns through FDs.
• It faster than you think. If you are to save Rs 5 a month, earn 5% interest compounded each month, and doing this continuously for 10 years, you would have Rs 600 in your account, but the account would be worth Rs 776. And, even if you don’t add a single rupee, it would still be worth Rs 1,500 by the next 15 years.
• Time is not on your side. Credit cards and loans levy compound interest. That's why paying just the minimum payments would increase your debt.

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