## What is Simple Interest?

This is the charge which is imposed by the lender of money to the borrower for separating with their funds which could have been diverted elsewhere. Simple Interest is computed on the Principal amount or on the amount of principal required to be paid off and is generally associated with loans which are short term in nature. It can be implemented on a yearly, monthly and daily basis.

### Simple Interest Formula

**The formula to calculate simple interest is:**

Simple Interest Formula = (P x R x T)/100

*whereby SI = Simple Interest

- P= Principal
- R= Rate of Interest
- T= Time period

### Simple Interest Examples

#### Simple Interest Example # 1

Let us consider the below example for a clearer understanding:

If Mr. A. borrows INR 10,000 from Mr. B. @ 8% for 5 years then at the end of 5^{th} year Mr. A has to pay:

SI = 10,000*8*5 = INR 400/100

The amount of INR 4000 is the Interest amount which has to be paid in addition to the Principal amount of INR 10,000. Thus, the final Amount = INR 10,000 + INR 4000 = INR 14,000.

All the above mentioned components play an important role in arrival of the interest amount. If any of the component increases or decreases, it will have a direct impact on the final result.

Simple Interest is usually applicable to Short-term personal loans or Automobile loans which generally have fixed time payment and not a very large amount of Principal to pay off. Since Simple interest is computed on a daily basis, it is mostly beneficial for customers who make their loan payments on a fixed date/monthly basis.

#### Simple Interest Example # 2

Mr. Z. borrowed $12,000 at 10% SI (Simple Interest) and lent the same sum of money to Mr. P. @ 15%. What will be the gain after 5 years?

Since the rate of borrowing was 10% and lending rate is 15%, the gain is actually 5% [15% – 10%] for 1 year. Thus, to arrive at the gain, this difference is used as the ROI.

Given that T = 5 years and P = $12,000, the amount gained = $12,000 * 5 * 5% = $3,000

### Installment and Simple Interests

The concept of the installment is extensively used in the finance world. When an individual wants to purchase a product, it is possible the individual may not have sufficient money to buy immediately. However, they can spread out the payment schedule over a given time frame i.e. make equal payments over the duration. Since instalments are after a fixed interval, the lender is losing out on the opportunity of enhancing the money which could have fetched him more returns had the entire payment made at the time of initiation.

To compensate for the same, when every installment is made, a component of interest is also included with the Principal money as the Time, Value of Money.

**Let us consider the below example:**

What is the annual installment to discharge a debt of $7,700 due in 5 years with an ROI of 5%?

The installment paid at the end of the 1^{st}, 2^{nd}, 3^{rd}, 4^{th} and 5^{th} year shall result in the Simple interest paid for 4, 3,2,1,0 years respectively.

Let us start with an assumption that the downpayment is of $1000.

- At the end of 1
^{st}year, amount paid will be = $1000 + {(5*4*100)/100} = $1020 - At the end of 2
^{nd}year, amount paid will be = $1000 + {(5*3*100)/100} = $1015 - At the end of 3
^{rd}year, amount paid will be = $1000 + {(5*2*100)/100} = $1010 - At the end of 4
^{th}year, amount paid will be = $1000 + {(5*1*100)/100} = $1005 - At the end of 5
^{th}year, amount paid will be = $1000

Thus, total amount paid = 1020+1015+1010+1005+1000 = $5050

This implies that for an amount of $5050, the annual instalment is $1,000 and therefore, for $7,700 the annual instalment with the component of Simple Interest:

(1000 * 7700) / 5050 = $1,524.75

In certain circumstances, the interest will not necessarily be charged on a yearly basis but could be quarterly, monthly or even a daily basis.

**Let us look into another example:**

A person lends $10,000 to a Corporation by purchasing a bond from them. Simple interest is computed on a quarterly basis at 3 percent per quarter, and a cheque for the interest is sent across every quarter to all the bondholders. The bonds expire at the end of 5 years, and the final cheque includes the original principle plus interest earned during the last quarter. What is the interest for every quarter and what will be the total interest earned over 5-year life of the bonds?

Given that P=$10,000, ROI = 0.03 per quarter with a time frame of 5 years. As the time period is on a quarterly basis, we shall consider 5 years = 20 quarters. Thus, quarterly interest:

SI = $10,000 * 0.03 * 1 = $300 for every quarter. Therefore, interest for 20 quarters = $300 * 20 = $6,000

### Simple Interest vs Compound Interest

The concept of compound interest is used synonymously with Simple interest since it is a more accurate description of the interest amount earned. Let us study some of the differences between simple interest vs compound interest:

Simple Interest |
Compound Interest |

It is the interest amount computed as a fixed percentage of the Principal amount. | Interest amount as a percentage of the principal amount and the accumulated interest. It’s like Interest on Interest. |

The returns computed are less | Returns are on the higher side |

The principal remains constant | The principal keeps on changing during the duration of borrowing. The amount keeps on accumulating. |

Formula of Simple Interest = [P*R*T / 100] | Formula of Compound Interest = P*[1+r]^{t} |

Payment first goes towards interest component and remainder on the principal | Some of the monthly interest is added back to the loan for every succeeding month. Interest is paid on the old interest. |

Simple Interest is charged on the Principal amount | Compound Interest is imposed on Principal and the Accumulated Interest |

Simple Interest concept is utilized on Small term loans, automobile loans etc | Compound Interest concept is used by Banks, Financial institutions on Deposits etc. |

### Conclusion

Though Simple interest is an easy and a simple tool for estimation of the interest earned or paid on a given Principal amount for a given time frame, it does not take into consideration the impact of compounding (the process of earning interest on principal plus interest amount earner previously). This can understate the amount of interest earned or paid over time.

### Additional Resources

Hope you liked the Simple Interest Guide and also the differences between Simple Interest vs Compound Interest. You may also look at below articles to learn Corporate Finance

- Time Value of Money
- Weighted Average Cost of Capital (WACC)
- Dividend Discount Model Guide
- Corporate Finance Career Options

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