Simple Interest: Definition, Formula, Question, Examples, Calculator

Simple interest is a fundamental concept in finance and mathematics that refers to the cost of borrowing money or the return on investment over some time. This method of calculating interest is straightforward and widely used in various financial transactions, including loans, savings accounts, and investments. Understanding the simple interest formula is crucial for accurately calculating interest in these contexts. Additionally, using tools like a simple interest calculator or implementing the simple interest formula in Excel sheet can simplify these calculations. This article will explore the concept of simple interest, its calculation methods, and its applications, including simple interest and compound interest problems and solutions. We will also discuss the simple interest and compound interest differences.

What is Simple Interest?

Simple interest is the type of interest that is calculated on the principal amount of a loan or an investment, without considering any previously earned interest. It is a fixed percentage of the principal amount over a specified time.

For example, Think about a time when you borrowed money from your siblings after your pocket money ran out, or when you lent them some money. When you borrow, you use the money for your intended purpose and then repay it when you receive your next month's pocket money. This is a simple example of borrowing and lending within a family.

In the real world, borrowing money isn't free. When you take out a loan from a bank, you not only repay the principal amount but also an additional amount called interest. This interest depends on both the loan amount and the period for which you borrow. This additional cost is called simple interest. Simple interest is widely used in banking and finance for its ease of calculation and transparency.

How do you calculate Simple interest?

The formula to calculate simple interest is very simple to understand. We can calculate simple interest using the following formula:

SI = $\frac{P×R×T}{100}$

Where SI = Simple Interest

P = Principal

R = Rate of interest (in percentage)

T = Time (in years)

Let’s understand these terms in more detail,

• Principal: The initial sum of money lent or invested. It is denoted by P.

• Rate of Interest (R): The rate of interest is the rate at which the principal amount is given to someone for a certain time. It is denoted by R.

• Time (T): The duration for which the money is borrowed or invested. It is denoted by T.

We can also calculate the total amount (A) using the formula:

A = P + SI, where, A is the amount, P is the principal and SI is the simple interest.

Example: If a man borrows Rs.5000 at an annual interest rate of 4% for 5 years then, find the simple interest.

⇒ Here, principal (P) = Rs.5000

Annual rate of interest (R) = 4%

Time (T) = 5 years

So, the simple interest = $\frac{P×R×T}{100}$ = $\frac{5000×4×5}{100}$ = Rs.1000

How to Calculate Simple Interest if the time is in months?

When the time is given in months, then we have to divide it by 12 to convert it into years. After that, we can use the simple interest formula to calculate the interest.

Example: Find the simple interest of Rs.10,000 at the annual interest rate of 3% for 6 months.

Solution: Here, principal (P) = Rs.10,000

Annual rate of interest (R) = 3%

Time (T) = 6 months = $\frac{6}{12}$ years = $\frac{1}{2}$ years

So, the simple interest = $\frac{P×R×T}{100}$

= $\frac{10,000×3×\frac{1}{2}}{100}$

= Rs.150

How to Calculate Simple Interest if the time is in days?

When the time is given in days, then we have to divide it by 365 to convert it into years. After that, we can use the simple interest formula to calculate the interest.

Example: Find the simple interest of Rs.50,000 at the annual interest rate of 10% for 100 days.

Solution: Here, principal (P) = Rs.50,000

Annual rate of interest (R) = 10%

Time (T) = 100 days = $\frac{100}{365}$ years = $\frac{20}{73}$ years

So, the simple interest = $\frac{P×R×T}{100}$

= $\frac{50,000×10×\frac{20}{73}}{100}$

= Rs.1369.84

Comparison with compound interest

Simple interest and compound interest are two different methods of calculating interest. The key difference is that simple interest is calculated on the principal amount only, whereas compound interest is calculated on the principal plus any previously earned interest.

The formula of simple interest = $\frac{P×R×T}{100}$

The formula of compound interest = $P[(1+\frac{\frac{R}{n}}{100})^{nT} - 1]$, where P and R are the principal and the annual rate of interest while T is the number of years and n is the number of compounding periods per year.

For more information about compound interest click here.

Use of Simple interest to calculate depreciation:

Simple interest can also be used to calculate depreciation, which is the reduction in value of an asset over time.

Example: A machine is purchased for Rs.5,000 and depreciates at a rate of 10% per year. Find the value of the machine after 3 years.

Solution: Here, principal (P) = Rs.5000

Annual rate of depreciation (R) = 10%

Time (T) = 3 years

So, the depreciation value after 3 years = $\frac{P×R×T}{100}$

= $\frac{5,000×3×10}{100}$

= Rs.1500

Therefore, the value of the machine after 3 years = (5000 - 1500) = Rs.3500.

Applications of Simple Interest

Simple interest has various practical applications, including:

• Personal Loans: One of the most common applications of simple interest is in personal loans. When individuals borrow money from a bank or financial institution, the interest on these loans is often calculated using the simple interest formula. This makes it easier for borrowers to understand how much they will have to pay in total.

• Savings Accounts and Fixed Deposits: Banks and financial institutions often use simple interest to calculate the interest earned on savings accounts and fixed deposits. This application allows the account holder to predict their earnings over a specified period accurately.

• Investment: Simple interest is used to calculate the returns on certain types of bonds and other fixed-income investments. Investors can quickly assess their expected earnings from such investments.

• Depreciation: Simple interest can also be used to estimate the depreciation of an asset over time. This application is particularly useful for accounting and tax purposes.

Tips and Tricks

• Understand the simple interest formula and have a clear idea about each of the terms.

• Interest rates are often given as percentages. Convert the percentage to a decimal for ease of calculation by dividing by 100. For example, 5% becomes $\frac{5}{100}$ = 0.05.

• Make sure the time frame is in years. If the time is given in months or days, convert it to years by dividing by 12 or 365, respectively.

• Break down the calculation into smaller steps to avoid mistakes. First, convert the rate and time if necessary, then apply the formula.

• Numerous online simple interest calculators are available that can quickly compute the interest for you. These tools are useful for verifying your manual calculations.

• When calculating interest over days, remember that leap years have 366 days. This can slightly affect your calculation for long-term investments or loans.

Practice Questions/Solved Examples on Simple Interest

Q.1.

The simple interest on a sum for 5 years is $\frac{3}{5}$th of the sum. The rate of interest per annum is:

1. 10%

2. 12%

3. 8%

4. $12\frac{1}{2}$%

Hint: Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

Solution:

Let the principal be $x$.

⇒ Simple interest $=\frac{3x}{5}$

Also, Simple interest $=\frac{\text{Principal × Rate × Time}}{100}$

⇒ $\frac{3x}{5}=\frac{x×\ \text{Rate}\ ×5}{100}$

⇒ Rate $=\frac{3x×100}{5×x×5}$

$\therefore$ Rate = 12%

Hence, the correct answer is option (2).

Q.2.

A person deposited Rs. 500 for 4 years and Rs. 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs. 190 as interest. The rate of simple interest per annum was:

1. 4%

2. 5%

3. 2%

4. 3%

Hint: Use this formula:

$SI=\frac{P×R×T}{100}$, where $SI$ is the interest, $P$ is the principal amount, $R$ is the rate of interest and $T$ is the time in years.

Solution:

The formula for simple interest is $SI=\frac{P×R×T}{100}$, where $SI$ is the interest, $P$ is the principal amount, $R$ is the rate of interest, and $T$ is the time in years.

Given that a person deposited Rs. 500 for 4 years and Rs. 600 for 3 years and received Rs. 190 as interest altogether.

So, $\frac{500×4×R}{100}+\frac{600×3×R}{100}=190$

$⇒20R+18R=190$

$⇒38R=190$

$⇒R=5$%

Hence, the correct answer is option (2).

Q.3.

At a certain time, the ratio of a certain principal and the simple interest obtained from it are in the ratio 10 : 3 at 10% interest per annum. The number of years the money was invested is:

1. 1

2. 3

3. 5

4. 7

Hint: Use this formula:

Simple interest (SI) = $\frac{P×R×T}{100}$, where $P$ is the principal amount, $R$ is the rate of interest per annum and $T$ is the time in years.

Solution:

Given: The ratio of a certain principal and the simple interest obtained from it are in the ratio 10 : 3 at 10% interest per annum.

Simple interest (SI) = $\frac{P×R×T}{100}$, where $P$ is the principal amount, $R$ is the rate of interest per annum, and $T$ is the time in years.

According to the question,

Let principal = $10x$, SI = $3x$, and rate = 10%

So, $3x =\frac{10x\times T\times 10 }{100}$

⇒ $T = \frac{3x \times 100}{10x \times 10} = 3$ years

Hence, the correct answer is option (2).

Q.4.

At the same rate of simple interest sum of the interest of Rs. 300 for 4 years and the interest of Rs. 400 for 3 years is 120. The rate of interest is:

1. 5%

2. 4%

3. 6%

4. 10%

Hint: Use this formula:

Simple interest (SI) = $\frac{P×R×T}{100}$ where $P$ is the principal amount, $R$ is the rate of interest per annum and $T$ is the time in years.

Solution:

Given: At the same rate of simple interest, the sum of the interest of 300 for 4 years and the interest of 400 for 3 years is 120.

We know that simple interest (SI) = $\frac{P×R×T}{100}$ Where $P$ is the principal amount, $R$ is the rate of interest per annum and $T$ is the time in years.

So, $\frac{300 \times R\times 4}{100} + \frac{400 \times R\times 3}{100} =120$

⇒ $12R + 12R = 120$

⇒ $24R = 120$

⇒ $R = \frac{120}{24}$

⇒ $R = 5$%

Hence, the correct answer is option (1).

Q.5.

A sum was doubled with a 12.5% rate of simple interest per annum. The time taken for that sum to be doubled is:

1. $8\frac{1}{2}$ years

2. 8 years

3. 10 years

4. $12\frac{1}{2}$ years

Hint: Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

Solution:

Let the principal be $P$.

Sum = $2P$

Let the time be $T$.

$\therefore$ Simple interest = Amount – Principal = $2P-P=P$

We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

⇒ $T=\frac{P×100}{P×12.5}$

⇒ $T=\frac{1000}{125}$

$\therefore T$ = 8 years

Hence, the correct answer is option (2).

Q.6.

A sum was lent at simple interest at a certain rate of 2 years. Had it been lent at a 3% higher rate, it would have fetched Rs. 300 more. The original sum of money was:

1. Rs.5000

2. Rs.6000

3. Rs.7000

4. Rs.4000

Hint: Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

Solution:

Given: A sum was lent at simple interest at a certain rate of 2 years. Had it been lent at a 3% higher rate, it would have fetched 300 more.

We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

Let the rate be $R$% and the increased rate be $(R+3)$%.

So, $\frac{P\times (R+3) \times 2}{100}-\frac{P \times R \times 2}{100}= 300$

⇒ $\frac{P \times 2}{100}×(R+3-R) = 300$

⇒ $\frac{P\times 2\times 3}{100} = 300$

$\therefore P =$ Rs. 5000

Hence, the correct answer is option (1).

Q.7.

A sum of Rs. 2,400 amounts to Rs. 3,264 in 4 years at a certain rate of simple interest. If the rate of interest is increased by 1%, the same sum at the same time would amount to:

1. Rs. 3,288

2. Rs. 3,312

3. Rs. 3,340

4. Rs. 3,360

Hint: Use this formula:

Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

Solution:

Given: Principal = Rs. 2400 and amount = Rs. 3264

We know, Rate of interest = $\frac{\text{Simple interest}\times 100}{\text{Principal} \times \text{Time}}$

Simple Interest, SI = Rs. 3264 – Rs. 2400 = Rs. 864

So, the rate = $\frac{\text{SI}\times 100}{\text{Principal} \times \text{Time}}$

⇒ Rate = $\frac{\text{864}\times 100}{\text{2400} \times \text{4}} = 9$% per annum

New Rate = 9% + 1% = 10% per annum

So, SI = $\frac{2400 \times 10\times 4}{100} = $ Rs. $960$

Amount = Rs. 2400 + Rs. 960 = Rs. 3,360

Hence, the correct answer is option (4).

Q.8.

Rs. 2300 is invested for 3 years in a scheme of simple interest at a rate of 12% per annum. What is the amount obtained (in Rs.) after 3 years?

1. Rs. 3128

2. Rs. 3456

3. Rs. 3724

4. Rs. 2950

Hint: Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

Solution:

Given:

Principal = Rs. 2300

Rate = 3% per annum

Time = 12 years

We know,

Simple interest, SI = $\frac{\text{Principal × Rate × Time}}{100}$

⇒ SI = $\frac{2300 \times 3\times 12}{100}$ = Rs. 828

Amount obtained = Rs. 2300 + Rs. 828 = Rs. 3128

Hence, the correct answer is option (1).

Q.9.

At simple interest, a sum of INR 6,400 becomes INR 8,320 in 3 years. What will INR 7,200 become in 5 years at the same rate?

1. INR 10,200

2. INR 10,600

3. INR 10,800

4. INR 10,400

Hint: Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

Solution:

At simple interest, a sum of INR 6,400 becomes INR 8,320 in 3 years.

Simple interest = INR 8320 – INR 6,400 = INR 1,920

We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

⇒ Rate $ = \frac{1920 \times 100}{6400 \times 3} = 10\%$

Simple Interest on INR 7,200 = $\frac{\text{Principal × Rate × Time}}{100}=\frac{7200×10×5}{100}$ = INR 3,600

$\therefore$ Amount = INR 7200 + INR 3600 = INR 10,800

Hence, the correct answer is option (3).

Q.10.

A person borrowed some money at simple interest. After 4 years, he returned $\frac{9}{5}$th of the money to the lender. What was the rate of interest?

1. 25% per annum

2. 10% per annum

3. 15% per annum

4. 20% per annum

Hint: Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$

Solution:

Let the amount of money borrowed $=x$

The amount he returned to the lender $= \frac{9}{5}x$

Simple Interest $ = \frac{9}{5}x - x = \frac{4}{5}x$

Time = 4 years

We know, Simple interest $=\frac{\text{Principal × Rate × Time}}{100} = \frac{x\times \text{Rate}\times 4}{100}$

⇒ $\frac{4}{5} x=\frac{x\times \text{Rate}\times 4}{100}$

$\therefore$ Rate = 20%

Hence, the correct answer is option (4).

Answer:

Simple interest and compound interest are two different methods of calculating interest. The key difference is that simple interest is calculated on the principal amount only, whereas compound interest is calculated on the principal plus any previously earned interest.