## An Overview

The rate of interest is the percentage of principal that a lender charges to a borrower. Different banks provide different rates of interest. Simple interest is very commonly used in our daily lives. The rate of interest is always taken as a fraction in the formula for simple interest. In this article, we will discuss about what is simple interest and the formula for calculating simple interest.

## What is Simple Interest?

Before we learn the formula for rate in simple interest, we will first learn what simple interest is. Simple interest is a method to calculate the interest gained over a particular sum, at a specific rate in a given period of time. The interest is applied on the amount (principal) you invest in the bank at a fixed interest rate. The formula for calculating simple interest is \[\]\[\left[ {{\text{simple interest}}} \right] = \left[ {{\text{Principal}}} \right] \times \left[ {{\text{percent rate of interest per annum}}} \right] \times \left[ {{\text{time}}} \right]\].

Simple Interest

## The Formula for Simple Interest

Simple interest is simply calculated using the following formula.

\[{\rm{S}}{\rm{.I = P}} \times {\rm{R}} \times \dfrac{T}{{100}}\] (As R is in percent)

Here, S.I. = Simple interest

\[{\text{p = principal amount }}\]

R = rate of interest in % per annum

T = The duration for which the money is invested.

Amount = It is the total money gained after the investment duration is over. It is calculated as \[{\text{Amount = Principal + Simple Interest }}\]

Formula for Simple Interest and Its Components

## Rate of Interest in Simple Interest

The rate of interest is the percentage of principal that a lender charges to a borrower. A 5% rate of interest means you will be charged 5% of the amount you have invested/ loaned from the lender, each year for the given time period. For example, a 2% rate of interest on Rs. 100,000 for 4 years means you will be charged 2% of 100,000 which is 2,000 per year for 4 years. The simple interest here will be \[{\rm{S}}{\rm{.I = 100000}} \times {\rm{[2\% ]}} \times {\rm{4 = 8000}}\]. Thus, the total payable amount will be \[{\text{Principal + }}\] \[{\rm{S}}{\rm{.I = 100000 + 8000}}\] = Rs. 108,000.

## The Formula for Rate of Interest in Simple Interest

These are the steps to find the rate of interest.

We first start with a formula for simple interest.

Then we make the rate of interest the subject of the equation and isolate it.

This will give us the formula for the rate of interest. Remember that the rate of interest is always kept a fraction in formulas.

Rate of interest %= \[\dfrac{\text{Simple interest}}{\text{principal} \times \text{time}}\]

Simple Interest and Its Components

We have learned about simple interests and their components. We have successfully understood the formula of simple interest and how its components work. We learned how the rate of interest practically works and how to calculate the rate of interest from the formula for simple interest.

## Solved Examples

1. Find the rate of interest if the simple interest is given to be Rs. 4,000 on a principal of Rs. 50,000 for 2 years.

Solution: We are given simple interest, principal amount, and the time period. We are required to find the rate of interest. Using the formula for rate of interest in the simple interest, we get

\[\dfrac{R}{{100}} = \dfrac{{[{\rm{S}}{\rm{.I]}}}}{P \times T}\]

\[\dfrac{R}{{100}} = \dfrac{{\left[ {4000} \right]}}{{\left[ {50000 \times 2} \right]}}\]

The above equation gives

\[\dfrac{R}{{100}} = 0.04\]

Hence, \[R = 4\% \]

2. Find the rate of interest if the total amount at the end of the interest period is given to be Rs. 640,000 on the principal amount of Rs. 500,000 for 7 years.

Solution: We start with writing down the formula for the amount.

\[{\text{Amount = principal + simple interest}}\]

\[{\text{Amount = principal + principal}} \times {\rm{rate}} \times {\rm{time}}\]

Now we put down the values we already have been given,

\[640000 = 500000 + 500000 \times \dfrac{R}{{100}} \times 7\]

or,

\[\dfrac{R}{{100}} \times 7 = \dfrac{{140000}}{{500000}} = \dfrac{{14}}{{50}}\]

\[\dfrac{R}{{100}}= \dfrac{2}{{50}} = 0.04\]

This gives,

\[R =4\% \]

## Conclusion

Simple interest is very commonly used in our daily lives. Banks use this method daily to provide loans to customers. We have learned how important simple interests are and how we can calculate them. We also learned how to calculate different components (Principal, Rate of interest, and time period) if any three of the quantities are given.

## FAQs on Rate of Interest in Simple Interest

1. Is it safe if banks give negative interest rates?

Normally banks lend us money and charge us interest on the principal amount. This happens when we are offered a positive rate of interest. That means in the case of a negative rate of interest, the interest made will be given to the customer by the bank. In this case, the flow of money (interest made) is the opposite, instead of banks gaining the interests made, the customers gain the interests made. So, yes, it is safe if the bank provides negative interest rates.

2. What is the rate of interest?

The rate of interest is the percentage of principal that a lender charges to a borrower. It is calculated on the principle that a customer invests or borrows.

3. What is simple interest?

Simple interest is a method to calculate the interest gained over a particular sum, at a specific rate in a given period of time. It is the extra money that a customer has to pay at the end of a loan period.

4. Are the amount and principal amounts different?

Yes, the principal amount is the money that is being invested or loaned by the customer whereas the amount or total amount is the principal amount plus the simple interest charged or gained at the end of the interest period.

5. You want to borrow money to buy a car. Bank A is offering a 5% interest rate per annum while Bank B is offering a 4% interest rate. Which one should you choose?

When talking about interest rates, it is always best to go with a low-interest rate if you are taking a loan and high-interest rates when you are investing your money to get a higher output.