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Interest is calculated on the investment or loan taken. There are two ways one can calculate interest. The two ways are simple interest (SI) and compound interest (SI). Simple interest is basically the interest on a loan or investment. It is calculated on the principal amount. At the same time, CI is the interest on interest. It is calculated on the principal amount as well as the previous period’s interest. This article covers the difference between simple interest and compound interest in detail.

## What is a Simple Interest?

Simple interest (SI) is the cost of borrowing. It is the interest only on the principal amount as a percentage of the principal amount. Borrowers will benefit from simple interest as they have to pay interest only on loans taken. In other words, simple interest is the amount that one pays to the borrower for using the borrowed money for a fixed period.

One can easily compute Simple interest by multiplying the interest amount with the tenure and the principal amount. Simple interest doesn’t consider the previous interest. It is simply based on the original contribution amount.

Car loans and consumer loans use simple interest while estimating the interest payments. Even a certificate of deposit uses simple interest to calculate the return from the investment.

Borrowers benefit more from simple interest as there is no power of compounding. In other words, there is no interest on interest. However, investors might lose if their investments are based on simple interest.

## What is the formula for Simple interest?

Simple interest is computed by multiplying the interest rate for a period by the principal amount and the tenure. The tenure can be in days, months, or years. Hence the interest rate has to be converted accordingly before multiplying with the principal amount and tenure.

One can use the following formula to calculate the simple interest:

Simple Interest = P*I*N

Where,

P – Principal Amount

I – Interest Rate for the period

N – Tenure

#### Example 1

Let’s understand simple interest with an example. Ms Devika invests INR 1,00,000 in a fixed deposit for a tenure of three years at a 7% interest rate. Using the formula of simple interest, we can calculate the interest Ms Devika will earn from the investment.

Simple Interest = INR 1,00,000*7%*3 years

Simple Interest = INR 21,000

For her investment, Ms Devika receives INR 21,000 at the end of three years (investment tenure). The bank or the financial institutions pays Ms Devika an interest of 7% for using her deposit amount for its operations during the tenure of her investment (three years). The INR 7,000 is the interest that Ms Devika receives on her deposit from the borrower.

The simple interest should be calculated according to the duration of the investment or loan. If a loan is only for a few days or months, the interest rate has to be converted into a daily or monthly basis. Let’s take an example of a loan that charges interest on a daily basis to understand it better.

#### Example 2

The principal amount of a loan is INR 50,000, of tenure of 60 days, with an interest rate of 5% per annum. One can compute the simple interest, in this case, as follows.

Principal amount – INR 50,000

Tenure – 60 days

Interest rate – 5% per annum or 0.014% per day.

Simple interest = INR 410.95

Therefore, the total interest the borrower will pay for the INR 50,000 loan for a tenure of 60 days is INR 410.95.

It is important to note that the higher the amount, the higher will be the interest. Also, the higher the duration of the investments, the greater will be the interest.

## What is compound interest?

Unlike simple interest, which gains interest only on the principal sum, compound interest (CI) earns interest on the previously earned interest. The interest is added to the principal amount. CI is simply Interest on Interest. The whole principle revolves around generating high returns by compounding the interest received on the principal sum.

In other words, CI has the potential to earn more return than just the simple interest from an investment. The investments grow exponentially with compound interest because it is based on the principal power of compounding.

The bank or financial institution, or the lender decide on the frequency of compounding. It can be daily, monthly, quarterly, half-yearly or yearly. The higher the frequency of compounding, the higher will be the interest accrual amount. Hence, investors benefit from compound interest more than borrowers.

Banks use compound interest for some loans. But compound interest is most commonly used in investments. Also, compound interest is used by fixed deposits, mutual funds, and any other investment that has reinvestment of profits.

## What is the formula for compound interest?

CI is calculated by multiplying one plus interest raised to the power of the compounding periods with the principal amount. Finally, the principal amount has to be subtracted to obtain the CI.

One can use the following formula to calculate compound interest:

A=P(1+r/n)^(n*t)-1)

Where,

A – Compound Interest

P – Principal Amount

r – the rate of interest

n – the number of compounding periods

t – number of years (duration)

#### Example 1

Let’s understand CI calculation with an example. Mr Charan invests INR 10,000 at the rate of 10% for five years. One can compute the CI using the formula.

A = 10000*((1+10%)^(5)-1)

A = INR 6,105.

The interest earned by Mr Charan is INR 6,105. The corpus at the end of his investment tenure is INR 16,105 (the principal and the interest). On the other hand, the simple interest for the same investment and tenure is INR 5,000. The difference between SI and CI amount is INR 1,105.

#### Example 2

If the frequency of compounding is higher, then the interest will be higher. Also, if the investment duration is higher, the returns will be higher as well. Let’s take the same example as above but with higher compounding periods to understand how the interest will be higher in this case.

Investment – INR 10,000

Interest – 10% per annum

Tenure – 5 years

Compounded – half yearly, therefore the compounding periods are 2

A = 10000*((1+10%/2)^(5*2)-1)

A = 10000*((1+5%)^(10)-1)

The CI in this case, for Mr Charan is INR 6289. The corpus at the end of his investment tenure is INR 16,289 (the principal and the interest). Mr Charan earned INR 183 extra in this case. Hence with higher compounding periods, the interest will also be higher.

Also, one can use the Scripbox’s Compound Interest Calculator to determine the values faster.

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## What is the power of compounding?

Compounding refers to a scenario where interest earns interest. It simply means when earnings are reinvested, the initial investment and the reinvested earnings grow at a constant rate. This makes the investments multiply at a faster rate. This is called the power of compounding. The higher the compounding frequency, the higher will be the returns from the investment. Compounding frequency is the number of times the interest is calculated in a year.

Compounding is a compelling concept, and no wonder Albert Einstein called it the 8^{th} wonder of the world. Under compounding, you can make your money work harder for you. The interest that accumulates earns more interest in the long term. Also, the longer you stay invested, the higher will be the return from an investment. Hence it is advisable to start investing at early ages to benefit from the power of compounding.

## Difference Between Simple Interest and Compound Interest?

Following are the key differences between simple interest vs compound interest:

Parameters | Simple Interest | Compound Interest |

Definition | Simple interest is the total amount paid to the borrower for using the borrowed money for a fixed period. | The compound interest earns interest on the previously earned interest and also the principal amount. |

Formula | Simple Interest = P*I*N | A=P(1+r/n)^(n*t) |

Interest Levied on | Principal amount | The principal amount and also the interest that accumulates |

Growth | Wealth grows steadily | Wealth growth is exponential due to compounding |

Returns | Lesser returns in comparison to compound interest | Higher returns in comparison to the simple interest |

Principal Amount | It remains the same with tenure | Principal increases. Interest gets compounded and gets added to the principal. |

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