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Simple Interest – Meaning, Formulas & Examples

what is simple interest

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

In this article, let’s understand what is simple 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). 

what is simple interest

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 $\text{A} = \text{P} + \text{S.I.} => \text{A} = \text{P} +\frac{\text{PRT}}{100} => \text{A} = \text{P} \left(1 + \frac{\text{RT}}{100} \right)$.

what is simple interest
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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 $12$.

what is simple interest

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 $365$.

what is simple interest

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} = $₹ $205.48$

Mixed Fraction to Improper Fraction

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.

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

what is simple interest

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 = $₹ $2,250$

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

$=>\text{R} = \frac {2,250\times100}{5,000\times5} = 9\%$

Ex 2: At what rate of interest will ₹$1,000$ will earn an interest of ₹$75$ in $9$ months?

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

Here, $\text{SI} = $₹ $75, \text{P} = $ ₹ $1,000,$ and $\text{T} = 9$ months = $\frac {9}{12} = \frac {3}{4}$ year 

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

$\text{R} = \frac {75\times100}{1,000\times \frac {3}{4}} = 10\%$

Calculating Time Period

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

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

what is simple interest

Examples

Ex 1: How much time will it take for an amount of ₹$450$ to yield ₹$81$ as interest at $4.5\%$ per annum of simple interest?

Here, $\text{P} = $₹ $450, \text{SI} = $₹ $81,$ and $\text{R} = 4.5\%$

$\text{T} = \frac {\text{SI}\times100}{\text{PR}} => \text{T} = \frac {81\times100}{450 \times 4.5} => \text{T} = 4$ years

Therefore, it will take $4$ years for an amount of ₹ $450$ to yield ₹ $81$ as interest at $4.5\%$ per annum of simple interest.

Ex 2: How much time will it take for an amount to double itself in simple interest at the rate of $10\%$ p.a.?

Let’s assume the principal amount as ₹$x$

Therefore, the amount = ₹$2x$ (Double the principal)

$=> \text{SI} = \text{A} – \text{P} = 2x – x = x$

$\text{T} = \frac {\text{SI}\times100}{\text{PR}}  => \text{T} = \frac {x\times100}{x \times10} = 10$ years

Calculating Principal

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

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

what is simple interest

Examples

Ex 1: A sum fetched a total simple interest of ₹$4016.25$ at the rate of $9\%$ p.a. in $5$ years. What is the sum?

Here, $\text{SI} = $₹ $4016.25, \text{R} = 9\%,$ and $\text{T} = 5$ years

$\text{P} = \frac {\text{SI}\times100}{\text{RT}} => \text{P} = \frac {4016.25\times100}{9\times5} = $₹ $8,925$

Therefore, ₹$8,925$ will fetch ₹$4016.25$ as simple interest at the rate of $9\%$ p.a. in $5$ years.

Advantages of Using 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.

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

Features of Simple Interest

Following are the characteristic features of simple interest.

  • Simple interest is what it costs to borrow money without compound interest, which is interest on the principal and on the interest.
  • Simple interest is calculated by looking at the principal amount borrowed, the rate of interest, and the time period it will cover.
  • Simple interest is more advantageous for borrowers than compound interest, as it keeps overall interest payments lower.
  • Car loans, amortized monthly, and retailer installment loans, also calculated monthly, are examples of simple interest; as the loan balance dips with each monthly payment, so does the interest.
  • Certificates of deposit (CDs) pay a specific amount in interest on a set date, representing simple interest.

Difference Between Simple Interest & Compound Interest

what is simple interest

Conclusion

Simple interest is a technique used to calculate the proportion of interest paid on a sum over a set time period at a set rate. The principal amount remains constant in simple interest. Simple interest is a straightforward and easy technique for calculating interest in money.

Following are the important formula related to simple interest:

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

Practice Problems

  1. How much time will it take for an amount of ₹$900$  to yield ₹$81$  as interest at $4.5\%$  per annum of simple interest?
  2. Arun took a loan of ₹$1400$ with simple interest for as many years as the rate of interest. If he paid ₹$686$ as interest at the end of the loan period, what was the rate of interest?
  3. A sum of money at simple interest amounts to ₹$815$ in $3$ years and to ₹$854$ in $4$ years. What is the sum?
  4. A sum fetched a total simple interest of ₹$929.20$ at the rate of $8\%$ per annum in $5$ years. What is the sum?
  5. Mr.Thomas invested an amount of ₹$13,900$ divided in two different schemes A and B at the simple interest rate of $14\%$ per annum and $11\%$ per annum respectively. If the total amount of simple interest earned in $2$ years was ₹$3508$, what was the amount invested in Scheme B?
  6. A person borrows ₹$5000$ for $2$ years at $4\%$  per annum simple interest. He immediately lends it to another person at $6 \frac {1}{4}\%$ per annum for $2$ years. Find his gain in the transaction per year.
  7. What is the ratio of simple interest earned by a certain amount at the same rate of interest for $5$ years and that for $15$ years?
  8. A sum of money amounts to ₹$9800$ after $5$ years and ₹$12005$ after $8$ years at the same rate of simple interest. Find the rate of interest.
  9. A certain amount earns a simple interest of ₹$1200$ after $10$ years. Had the interest been $2\%$ more, how much more interest would it have earned?
  10. A man took a loan from a bank at the rate of $8\%$ per annum with simple interest. After $4$ years he had to pay ₹$6200$ interest only for the period. What was the principal amount borrowed by him?

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FAQs

What is meant by the interest rate formula?

Using the interest rate formula, we get the interest rate, which is the percentage of the principal amount, charged by the lender or bank to the borrower for the use of its assets or money for a specific time period. The interest rate formula is $\text{Interest Rate} = \frac{\text{Simple Interest} \times 100}{\text{Principal} \times \text{Time}}$. 

What is the formula to calculate the interest rate?

The interest rate for a given amount on simple interest can be calculated by the following formula,
$\text{Interest Rate} = \frac{\text{Simple Interest} \times 100}{\text{Principal} \times \text{Time}}$
The interest rate formula in terms of compound interest is written as:
$\text{Compound Interest Rate} = \text{P} \left(1+ i \right)^{t} – \text{P}$
where, 
$\text{P}$ = principal amount
$i = r$ = rate of interest
$t$ = time period

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.

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