**“Compounding interest is the greatest mathematical discovery of all time" - Albert Einstein**

**These words by the great Albert Einstein say it all. And it how in reality is that the power of compounding makes wonders. We have seen bit information about compounding in the previous article; in this we will see it in detail.**

All of us must have learnt about compounding and its significance sometime in school. However, an interesting story which explained the power of compounding wonderfully. Here it is…

Once upon a time there was a king known for his generosity and keeping his word. A famous and intelligent prisoner was awaiting his death sentence and was brought in front of the king. The king was playing chess when the prisoner was brought in front of him. Here’s the dialogue that followed.

**King:**

*What is your last wish?*

**Prisoner:**

*Your Majesty, I wish to make provisions for my family to survive after my death.*

**King:**

*Well! Tell me what you want.*

Prisoner:

Prisoner:

*Give me the number of grains of rice on the last square of the chess board, if a single grain was kept on the first square and then doubled on every next square (1 on first, 2 on second, 4 on third, 8 on fourth, 16 on fifth and so on, till the 64th square), and I shall give it to my family before I die.*

**King:**

*(Thinking what a paltry demand the prisoner had made) Wish granted.*

The king then ordered his ministers to have the amount of rice calculated and given to the prisoner. But he was in for a rude surprise. The amount calculated was so large (18 million trillion grains of rice - more than enough to cover the entire surface of the earth) that the king lost his entire kingdom and was indebted to the prisoner all his life.

This can be true even in reality. When the interest on the principal amount is calculated and then added to the principal amount and calculated again in the same manner, we get

**compound interest**. The word compounding means made up of multiple parts.This means that when the interest is added to principal, the interest that is added earns interest too. This adding of the interest to the principal is termed

**compounding**. We can earn compound interest on a daily, weekly, monthly or yearly basis. The more times the amount is compounded, the more money is made for the investor.How compounding works?

**--- Final value = P(1 + R/T)^TY**

P = Principal

R = Rate of Interest

Y = Number of years you want to invest

T = Number of times your principal will compound

Example 1:

Suppose that you have deposited the sum of Rs.15000 in your bank and it pays a yearly interest rate of 5%, compounded on a quarterly basis. Now let us look at what the balance will be after a period of 5 years.

Using the above formula, with P = 15000, r = 5/100 = 0.050, t= 4 and y = 5:

**Principal**at the end of 5 years will be = 15000(1 + 0.050/4) ^20 = 19230.56

This means that an investment of 15,000 will grow to 19230.56 after a period of 5 years.

Example 2:

Assume an investment of Rs. 1000 in a

**fixed deposit**__for 3 years, at an interest rate of 10% p.a., compounded annually. Your interest earnings would be as under__Particulars | Amount at the beginning of the year | Interest Earned 10% p.a. | Balance at the year end |

Year 1 | 1,000 | 1,000*10% = 100 | 1,100 |

Year 2 | 1,100 | 1,100*10% = 110 | 1,210 |

Year 3 | 1,210 | 1,210*10% = 121 | 1,331 |

At the end of year 2, your interest is calculated on Rs. 1,100 and not Rs. 1,000. That’s where the brilliance of compounding comes into play. Had the simple interest principle been followed, you would have earned interest on Rs. 1000 and hence interest earned in year 2 would have been lower by Rs. 10 and in year 3 it would be lower by Rs. 21.

The above two illustrates if you want compounding works best for you, you need to make sure the two considerations :-

1) Time – Starting investing as early as possible

2) Frequency - The more frequent the compounding is done (i.e. daily, monthly, quarterly,

semi-annually and annually), the better it is.

Under the quarterly compounding option, the amount of money amassed is the highest, followed by semi-annual compounding, followed by annual compounding.

An amount of Rs. 20,000 invested in a fixed deposit at an interest of 10% p.a compounded at varied frequencies and for different tenures :-

Year | |||||

1 | 2 | 3 | 4 | 5 | |

Quarterly | 22076 | 24368 | 26898 | 29690 | 32772 |

Semi-Annually | 22050 | 24310 | 26802 | 29549 | 32578 |

Annually | 22000 | 24200 | 26620 | 29282 | 32210 |

See the difference of earnings in quarterly / Semi-annually and annually compounding. This is how the magic is!

With the above explanation, it is clear that compound interest helps you amass wealth by making your money work hard for you.

Albert Einstein rightly termed it the “Most Powerful Force on Earth.” The earlier you start investing, the richer compound interest will make you. Also next time, you look at any fixed interest instrument; make sure your interest is compounded at the maximum available frequency (In order - 1.Monthly, 2.Quarterly, 3.Semi-annually, 4.Annually).

So Is Compound Interest really the

**8th Wonder of the world**?From investor’s point of view - yes, it is. There is nothing in the world that can give investors this much return.

## No comments:

## Post a Comment