Interest is defined as the amount to be paid to the lender by the borrower on the principal loan. It can also be referred to as rate paid for the amount deposited as in the case of a certificate of deposit. Interest rate is the rate charged by the lender for the use of assets (could include cash, consumer goods, vehicles or building) denominated as a percentage of the principal.

All the lending and borrowing transactions carry their own interest rates and do have a great impact on markets, finance and economy. From the perspective of borrower, the interest rate is the cost of debt and the rate of return for the lender. Interests are basically calculated in two simple ways:

**Simple interest **It is calculated on the principal or the original amount of a loan.

Simple interest = P x R x T

P = Principal amount

R = Rate of interest

T = Term of the loan

**Compound interest** The word ‘compound’ itself means composed of two or more elements. Compound interest is not only calculated on the principal amount, but also on the interest rates.

Compound Interest = P x (1+R)^{ n}

P = Principal amount

R = Rate of interest

N = Number of years

Interest calculated via simple and compound methods differ in the amount payable on a loan.

Example: Let’s suppose you took Rs 1,00,000 as a student loan for your college tuition. Annual interest rate on this loan is 9% and duration is of 2 years. Let’s calculate the interest rates via both simple and compound methods.

**Via Simple Method Via Compound Method**

SI = P x R x T CI = P x (1+R) ^{n}

SI = 1,00,000 x 9/100 x 2 CI = 1,00,000 x (1+9/100)^{2}

SI = 18,000 CI = 18,810

Amount to be repaid = 1, 18,000 Amount to be repaid = 1,18,810

(Principal amount + SI) (Principal amount + CI)

So, the amount you need to pay at the end of two years calculated via simple interest method would be Rs 1,18,000 and via compounding would be Rs 1,18,810. Compound interests are always higher because it is calculated on both principal amount and accumulated interest rates. The compounded figures could be scary in case of debts, but could be quite desirable when it comes to investing and savings. The power and magic of compounding could be exploited and made to work in one’s favor with proper planning.

**How SI and CI work**

Compound interest makes deposit or loan to grow at a faster rate than simple interest, as it is calculated only on the principal amount, whereas compound interest on initial investment as well as interest rates incurred over time and so the compounding returns can help accumulate more and more and compounding is like interest on interest.

Example: Mr. A and Mr. B both deposit $10,000 in high-interest savings accounts at a rate of 5%. Mr A would like to go with less complicated simple interest and Mr B with compounding. Let’s see how their money would grow over years with their plans.

At the end of first year, both Mr. A and Mr. B would make $500 with 5% on their initial deposit. But for the subsequent years the return of investment would be different. Mr A would continue to make $500 or 5% of his initial investment of $10,000 each year. On the other hand, Mr B (as he has opted compounding) would not only be making 5% on his initial investment of $10,000, but also on his accumulated interest from previous periods.

So in year 2, Mr. B is going to earn 5% on both his principal as well as interest that he earned in year 1 rather than 5% on only his principal deposit of $10,000. With this in mind, Mr B will earn $525 in year 2 bringing his total capital to $11,025. Meanwhile, Mr. A will be earning $500 bringing his total capital to $11,000. By the end of year 2, Mr B has made $25 more than Mr. A.

In year 3, Mr. A is going to again make 5% of $10,000 with simple interest bringing his total capital to $11,500. While Mr. B will make 5% of $11,025 for an annual return of $551.25 bringing total capital to $11,576.25. So, after only two years Mr B has made $76.25 more than Mr A all due to compound interest.

### Compounding Periods:

Time Period | Mr A (Simple Interest) | Mr B (Compound Interest) |

Year 1 | $500 | $500 |

Year 2 | $500 | $525 |

Year 3 | $500 | $551.25 |

Year 4 | $500 | $578.81 |

Year 5 | $500 | $607.05 |

Year 6 | $500 | $638.14 |

Year 7 | $500 | $670.05 |

Year 8 | $500 | $703.55 |

Year 9 | $500 | $738.73 |

Year 10 | $500 | $775.66 |

While this might seem like an inconsequential amount of money, it is important to remember that the effect of compound interest increases over time. If we continue the above example, effects would be more profound when we look Mr. A and Mr. B return on investment over a 10-year horizon, with Mr B annual return accounting from $500 all the way to $775.66.

**Key Takeaways**

- With simple interest, the principal amount never changes with tenure, but in compound interest, the interest rates get added and the principal amount increases with increased tenure.
- Wealth accumulation is comparatively lower in SI than CI.
- Even slight increase in interest rate may increase the cost of borrowing in case of compound interest.
- Conversely, the power and magic of compounding can also generate higher returns if one invests in mutual funds or savings scheme that offer the option of earning compound interest trhough re-investments.

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