**Interest Formula (Table of Contents)**

## What is the Interest Formula?

This article will discuss the Interest Formula along with the Introduction and various Examples of Simple Interest and Compound Interest.

The term “interest” may refer to the income earned by the lender or the expense incurred by the borrower. Nevertheless, it is the amount that the borrower has to pay to the lender as a percentage of the loan amount.

The formula for simple interest can be derived as a product of outstanding loan amount, interest rate and tenure of the loan.

Formula For Simple Interest is represented as,

**Simple Interest = P * r * t**

where,

**P**= Outstanding Loan Amount**r**= Interest Rate**t**= Tenure of Loan

On the other hand, the formula for compound interest can be derived on the basis of the outstanding loan amount, interest rate, tenure of the loan and number of compounding per year.

Formula For Compound Interest is represented as,

**Compound Interest = P * [(1 + r/n)**

^{t*n}– 1]where,

**P**= Outstanding Loan Amount**r**= Interest Rate**t**= Tenure of Loan**n**= Number of Compounding Per Year

**Examples of Interest Formula (With Excel Template)**

Let’s take an example to understand the calculation of Interest in a better manner.

#### Interest Formula – Example #1

**Let us take a simple example of $1,000 borrowed by Travis from his friend Tony. Travis promised to pay a simple interest of 5% for three years, and then he will repay the loan to Tony. Calculate the interest to be incurred by Travis.**

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**Solution:**

Simple Interest is calculated using the formula given below

**Simple Interest = P * r * t**

- Simple Interest = $1,000 * 5% * 3
- Simple Interest =
**$150**

Therefore, Travis will incur an interest expense of **$150** during the loan tenure.

#### Interest Formula – Example #2

**Let us take the example of Dennis, who borrowed $2,000 from the bank. The bank charged interest at the rate of 7% compounded annually. The loan is for a period of 5 years. Calculate the interest expense to be incurred by Dennis.**

**Solution:**

Compound Interest is calculated using the formula given below

**Compound Interest = P * [(1 + r/n) ^{t*n} – 1]**

- Compound Interest = $2,000 * [(1 + 7%/1)
^{5*1}– 1] - Compound Interest =
**$805.10**

Therefore, Dennis will incur an interest expense of **$805** during the loan tenure.

#### Interest Formula– Example #3

**Let us take another example to understand the difference between simple interest and compound interest. Monty has decided to start a small hatchery for which is planning to borrow a sum of $5,000 for a period of 5 years. The lender has offered two options-**

**6.0% interest to be compounded annually****6.5% simple interest rate**

**Help Monty to decide which is a cheaper option for him.**

**1 ^{st} Option**

Compound Interest is calculated using the formula given below

**Compound Interest = P * [(1 + r/n) ^{t*n} – 1]**

- Compound Interest = $5,000 * [(1 + 6%/1)
^{5*1}– 1] - Compound Interest
**= $1,691.13**

**2 ^{nd} Option**

Simple Interest is calculated using the formula given below

**Simple Interest = P * r * t**

- Simple Interest = $5,000 * 6.5% * 5
- Simple Interest =
**$1,625**

Therefore, the 2^{nd} option is the cheaper one despite higher interest rates because the 1^{st} option is more expensive due to annual compounding.

### Explanation

Following are the steps to calculate Simple Interest:

**Step 1: **Firstly, determine the outstanding loan amount extended to the borrower, and it is denoted by ‘P’.

**Step 2:** Next, determine the interest rate to be paid by the borrower, and it is denoted by ‘r’.

**Step 3**: Next, determine the tenure of the loan or the period for which the loan has been extended. The tenure of the loan is denoted by ‘t’.

**Step 4:** Finally, the formula for simple interest can be derived as a product of outstanding loan amount (step 1), interest rate (step 2) and tenure of the loan (step 3) as shown below.

**Simple Interest = P * t * r**

Following are the steps to calculate Compound Interest:

**Step 1:** Firstly, determine the outstanding loan amount extended to the borrower, and it is denoted by ‘P’.

**Step 2:** Next, determine the interest rate to be paid by the borrower, and it is denoted by ‘r’.

**Step 3:** Next, determine the tenure of the loan or the period for which the loan has been extended. The tenure of the loan is denoted by ‘t’.

**Step 4: **Next, determine the number of compounding done per year, and it is denoted by ‘n’.

**Step 5: **Next, calculate the amount at the end of the loan tenure based on the outstanding loan amount (step 1), interest rate (step 2), tenure of the loan (step 3) and a number of compounding per year (step 4) as shown below.

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

**Step 6:** Finally, the formula for compound interest can be derived by deducting the initial outstanding loan amount from the amount at the end of the loan tenure calculated in the above step.

**Compound Interest = A – P**

**Compound Interest = P * (1 + r/n)**^{t*n}– P**Compound Interest = P * [(1 + r/n)**^{t*n}– 1]

### Relevance and Uses of Interest Formula

From the perspective of an analyst or accountant, the concept of interest expense is very important because it is used to manage the financial performance of any company. Interest calculation helps the companies to recognize the financial expense to be incurred over the entire tenure of the loan.

### Interest Formula Calculator

You can use the following interest Formula Calculator

P | |

r | |

t | |

Simple Interest | |

Simple Interest = | P x r x t |

= | 0 x 0 x 0 = 0 |

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