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# Simple Interest – Meaning, Formulas & Examples

July 25, 2022

Interest is the charge for borrowing money.  When an amount is borrowed, then the lender charges some amount extra and the borrower returns the borrowed amount along with the extra amount to the lender. This extra amount is called interest.

For example, a borrower borrows an amount of ₹$1,000$ from a borrower for a year. After one year, the borrower returns ₹$1,100$(for example) to the lender. This extra amount of ₹$100$ is the interest charged by the lender.

There are two main types of interests widely used

• Simple Interest
• Compound Interest

## What is the Rate of Interest?

An interest rate is the percentage of the amount charged by the lender for the use of its money. The amount on which the rate of interest is calculated is called the principal amount.

The rate of interest of $8\%$ means after the end of the period (usually one year), the interest will be $8\%$ of the principal amount.

For example, if the amount is ₹$100$, and the rate of interest is $8\%$, then the interest amount at the end of one year will be $100 \times \frac{8}{100}=$₹$8.00$. And for $2$ years it will be $2 \times 8 =$₹$16.00$.

## What is Simple Interest?

Simple interest is a quick and easy method to calculate interest on money.  In the simple interest method interest always applies to the original principal amount, with the same rate of interest for every time cycle (generally one year).

This interest is charged by the lender and paid by the borrower. You might have noticed that when you invest your money in any bank, it deposits an extra amount to your account. This extra amount you observe in your account at the end of a cycle is the interest.

## Simple Interest Formula

Simple interest is calculated using the formula: $\text{S.I.} = \text{P} \times \frac{\text{R}}{100} \times \text{T}$, where

$\text{P}$ = Principal amount. It is the amount initially borrowed from the bank or invested by the investor.

$\text{R}$ = Rate of interest in % per annum

$\text{T}$ = Time (number of years)

Simple interest is calculated using the formula: $\text{S.I.} = \text{P} \times \frac{\text{R}}{100} \times \text{T}$, where

$\text{P}$ = Principal amount. It is the amount initially borrowed from the bank or invested by the investor.

$\text{R}$ = Rate of interest in $\%$ per annum

$\text{T}$ = Time (number of years)

The total amount accumulated after the interest cycle is called the Amount and is denoted by the letter $\text{A}$, i.e., $\text{Amount} = \text{Principal} + \text{Simple Interest}$.

Hence, the formula for the amount becomes $\text{A} = \text{P} + \text{S.I.} => \text{A} = \text{P} +\frac{\text{PRT}}{100} => \text{A} = \text{P} \left(1 + \frac{\text{RT}}{100} \right)$.

Maths can be really interesting for kids

### Examples

Ex 1: What will be the simple interest on ₹$3,000$ in two years when the rate of interest is $5\%$?

$\text{P} =$₹$3,000$, $\text{R} = 5\%$, $\text{T} = 2 \text{years}$

$\text{SI} = 3,000 \times 5 \times \frac{2}{100} =$₹ $300$

And $\text{A} = 3,000 + 300 =$ ₹$3,300$.

Here the principal amount is ₹$3,000$, the time period is $2$ years and the rate of interest is $5\%$, therefore,

$\text{P} =$₹$3,000, \text{R} = 5\%, \text{T} = 2$ years

$\text{SI} = 3,000 \times 5 \times {2}{100} =$ ₹ $300$

And $\text{A} = 3,000 + 300 =$₹ $3,300$

Therefore, simple interest on ₹$3,000$ at the rate of $5\%$ per annum for $3$ years is ₹$300$ and the total amount is ₹$3,300$.

Ex 2: What will be the simple interest on ₹$5,500$ in five years when the rate of interest is $7.5\%$?

Here the principal amount is ₹$5,500$, the time period is $5$ years and the rate of interest is $7.5\%$, therefore,

$\text{P} =$₹$5,500, \text{R} = 7.5\%, \text{T} = 5$ years

$\text{SI} = 5,500 \times 7.5 \times \frac{5}{100} =$₹ $2062.50$

And $\text{A} = 5,500 + 2062.50 =$₹ $7562.50$

## Simple Interest – When Time is Not in Years

In the formula, $\text{SI} = \frac{\text{PRT}}{100}, \text{T}$ (time) is in years. But if the time period in the problem is in some other duration, then the first step is to convert time into years.

### Time in Months

Since there are $12$ months in a year, hence if the time period is given in months, it can be converted into years by dividing it by $12$.

#### Examples

Ex 1: Calculate simple interest on ₹$4,000$ for $5$ months at the rate of $10\%$ p.a.

Here the principal amount is ₹$4,000$, the time period is $5$ months and the rate of interest is $10\%$, therefore,

$P =$₹ $4,000, R = 10\%, T = 5$ months

$T = \frac {5}{12}$ year

$SI = \frac{4,000 \times 10 \times \frac{5}{12}}{100} =$₹ $166.67$

Ex 2: Calculate simple interest on ₹$2,000$ for $3$ months at the rate of $5\%$ p.a.

Here the principal amount is ₹$2,000$, the time period is $3$ months and the rate of interest is $5\%$, therefore,

$P =$₹ $2,000, R = 5\%, T = 3$ months

$T = \frac {3}{12} = \frac {1}{4}$ year

$SI = \frac {2,000 \times 5 \times \frac {1}{4}}{100} =$₹ $25$

### Time in Days

A year can have $365$ or $366$ days. But to make calculations simple, the number of days in a month is always taken as $365$. Thus, the time period in the number of days can be converted into a number of years by dividing it by $365$.

#### Examples

Ex 1: Calculate simple interest on ₹$1,000$ for $45$ days at the rate of $8\%$ p.a.

Here the principal amount is ₹$1,000$, the time period is $45$ days and the rate of interest is $8\%$, therefore,

$\text{P} =$₹ $1,000, \text{R} = 8\%, \text{T} = 45$ days

$\text{T} = \frac {45}{365}$ year

$\text{SI} = \frac {1,000 \times 8 \times \frac {45}{365}}{100} =$₹ $9.86$

Ex 2: Calculate simple interest on ₹$2,500$ for $250$ days at the rate of $12\%$ p.a.

Here the principal amount is ₹$2,500$, the time period is $250$ days and the rate of interest is $12\%$, therefore,

$\text{P} =$₹ $2,500, \text{R} = 12\%, \text{T} = 250$ days

$\text{T} = \frac {250}{365}$ year

$\text{SI} = \frac {2,500 \times 12 \times \frac {250}{365}}{100} =$₹ $205.48$

## Calculating Rate of Interest, Time, and Principal

You can use the formula $\text{S.I.} = \text{P} \times \frac {\text{R}}{100} \times \text{T}$ to find the rate of interest, time, or principal if you know the other three parameters.

### Calculating Rate of Interest

You can use the formula $\text{S.I.} = \text{P} \times \frac {\text{R}}{100} \times \text{T}$ to find the rate of interest in case the simple interest, principal, and time are known.

$\text{S.I.} = \text{P} \times \frac {\text{R}}{100} \times \text{T} => \text{R} = \frac {\text{SI}\times100}{\text{PT}}$.

#### Examples

Ex 1: At what rate of interest will ₹$5,000$ will amount to ₹$7,250$ in $5$ years?

$\text{R} = \frac {\text{SI}\times100}{\text{PT}}$

Here, $\text{A} =$₹ $7,250, \text{P} =$₹ $5,000,$ and $\text{T} = 5$ years

$\text{SI} = \text{A} – \text{P} = 7,250 – 5,000 =$₹ $2,250$

### What are the two main aspects of the interest rate formula?

The two main aspects to keep in mind while calculating the interest rate formula are simple interest and the principal. Simple interest talks about the amount while a loan is taken and the principal is the exact amount of money taken for a loan.