Simple Interest: Definition, Formulas, Solved Questions & Examples

Master the concept of simple interest and familiarize yourself with the formulas and techniques crucial for solving simple interest problems efficiently to prepare for your upcoming competitive exams.

Boost your knowledge and equip yourself with the skills needed to excel in your exams with a solid grasp of simple interest.

What is Simple Interest in Maths? 

Simple interest is the rate applied to the principal amount when borrowing or lending money. One of the key characteristics of simple interest is its linear growth. This means that the amount of interest earned or paid remains constant over time since it is based only on the original principal amount.

Simple Interest Formula Explained 

The formula to calculate simple interest is S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

This formula comprises some key elements:

• Principal amount (P): The initial sum of money lent, borrowed or invested. 

• Annual rate of interest (R): The percentage of interest charged by the lender on the amount lent. 

• Time (T): The length of time for which the interest is calculated, specified in days, months, or years.

• Amount (A): The amount is the total sum of money accumulated after adding the interest to the initial principal calculated by using the formula Amount= Principal+Interest. 

Simple Interest Formula for Years, Months & Days

Here's a table outlining the key differences between simple and compound interest:

In summary, simple interest is straightforward and calculated on the principal alone, while compound interest considers the interest on both the principal and the accumulated interest, leading to more significant growth over time.

Click here to enhance and upskill your quantitative aptitude by exploring different topics including simple interest and compound interest.

Simple Interest Examples & Practice Questions

Practice is the key to excelling in simple interest calculation! Provided below are some important selected questions with detailed answers:

Question 1. Calculate the simple interest earned on a principal amount of ₹5000 at an interest rate of 3% per annum for a period of 2 years.

Solution: To solve the question, we can use the formula:

Simple Interest = (Principal amount x Rate x Time)/100

Simple Interest = (5,000x3x2)/100= 30,000/100= 300

Therefore, the simple interest earned on a principal amount of ₹5,000 at an interest rate of 3% per annum for 2 years is ₹300.

Question 2: If ₹500 is invested at an annual interest rate of 4%, how much interest will be earned after 3 years?

Solution: Principal amount (P) = ₹500

Annual interest rate (R)= 4%= 0.04 Time

(T)= 3 years

Simple Interest (I)= P x R x T

= 500 x 0.04 x 3= 60

Therefore, the interest earned after 3 years will be ₹60.

Question 3: If ₹500 is invested at an annual simple interest rate of 8%, calculate the interest earned after 3 years.

Solution: Principal (P)= ₹500

Rate (R)= 8%

Time (T)= 3 years

Simple Interest (SI)= P x R x T / 100

=500x8x3 /100=120

Therefore, the interest earned after 3 years will be ₹120.

Question 4: If ₹5,000 is invested at an annual interest rate of 6%, how much interest will be earned after 3 years using simple interest?

Solution: Simple Interest = Principal (P) x Rate (R) x Time (T)

For the given question, the simple interest = 5,000 x 0.06 x 3= 900

Therefore, the total interest earned after 3 years would be ₹900.

Question 5: John invested ₹5,000 in a savings account for 3 years. In the first year, he earned a simple interest of 5%; in the second year, he earned 7%; and in the third year, he earned 10%. How much money did John have in his account at the end of the third year?

Solution: First-year simple interest = 5,000 x 5% = ₹250

Amount after first year = 5,000 + 250 = ₹5,250

Second-year interest = 5,250 x 7% = ₹367.50

Amount after second year = 5,250 + 367.50 =₹5,617.50

Third-year interest = 5,617.50 x 10% = ₹561.75

Total amount after third year = 5,617.50 + 561.75 = ₹6,179.25

Therefore, John had ₹6,179.25 in his account at the end of the third year.

Question 6: If you invest ₹5,000 in an account that offers a compound interest rate of 5% per year, how much money will you have after 5 years?

Solution: To solve this problem, we can use the formula for compound interest:

A=P×(1+n/r​)nt

Now, according to the question:

P = ₹5,000

r=5%=5/100=0.05

n=1 (interest compounded annually)

t=5 years

A=5,000×(1+0.05/1​)(1×5)

  =5,000×(1.05)5

A=5,000×(1.27628)

A≈6,381.40

So, after 5 years, you would have approximately ₹6,381.40 in the account.

Question 7: If you invest ₹8,000 in an account that offers a compound interest rate of 4% per year, compounded semi-annually, how much money will you have after 3 years?

Solution: According to the question,

• P = ₹8,000

• r=4%=0.04 (decimal)

• n=2 (interest compounded semi-annually)

• t=3 years

Putting these values into the formula:

A=8,000×(1+0.04/2​)(2×3)

A=8,000×(1.02)6

Now, calculate A:

A=8,000×(1.126825)

A≈9,014.60

So, after 3 years, you would have approximately ₹9,014.60 in the account.

Question 8: If you invest ₹10,000 with an annual interest rate of 6%, compounded quarterly, how much money will you have after 7 years?

Solution: According to the question, 

• P = ₹10,000

• r=6%=0.06 (decimal)

• n=4 (interest compounded quarterly)

• t=7 years

Plugging these values into the formula: A=P×(1+r/n​)nt

A=10,000×(1+0.06/4​)(4×7)

A=10,000×(1+0.06/4​)28

A=10,000×(1.015)28

A≈10,000×(1.662792)

A≈16,627.92

So, after 7 years, you would have approximately ₹16,627.92 in the account.

Question 9: Vikas borrowed ₹1,000 from a friend at an annual interest rate of 5%. How much interest will he owe after 2 years?

Solution: Interest=P×r×t

Given:

• Principal amount ₹1,000

• Annual interest rate 5% or 0.05

• Time 2 years

Substituting the given values into the formula:

Interest=1,000×0.05×2=1,000×0.1=100

So, Vikas will owe ₹100 in interest after 2 years.

Question 10: Samaj deposited ₹2000 into a savings account that offers an annual interest rate of 3.5%. How much interest will he earn after 1 year?

Solution: Interest=P×r×t

Given:

• Principal amount ₹2,000
• Annual interest rate 3.5% or 0.035
• Time 1 year

Substituting the given values into the formula:

Interest=2,000×0.035×1=70

So, Samaj will earn ₹70 in interest after 1 year.

Conclusion

For students preparing for competitive exams, mastering the simple interest formula and using simple interest calculators can be highly beneficial. Grasping the differences between simple and compound interest is essential for making informed decisions on financial questions that may appear on exams.

By grasping these concepts, students can approach questions related to interest calculations with confidence and accuracy, ultimately improving their performance in the exam.

Frequently Asked Questions (FAQs)

1. What is Simple Interest?

Simple interest is a basic type of interest calculated on the principal amount only. It does not take into account any accrued interest over time.

2. How is Simple Interest calculated?

To calculate simple interest, this formula is utilised: Simple Interest = Principal x Rate x Time. The result gives you the additional amount you will pay or receive based on the principal amount and rate.

3. What are the advantages of using Simple Interest calculators?

Simple interest calculators provide quick and accurate calculations for determining interest amounts. They are user-friendly tools that help individuals make informed financial decisions without complex mathematical computations.

4. List some practical applications of simple interest. 

Practical applications of simple interest include calculating interest on loans, determining returns on investments like fixed deposits, and understanding interest charges on credit card balances.

5. How does Simple Interest differ from Compound Interest?

Simple interest is calculated by taking into account only the original amount of money you started with. Compound interest considers both the initial amount and any interest earned so far when determining future interest payments.

6. What is the formula to calculate simple interest separately?

To compute the simple interest separately, subtract the principal from the total accrued amount using the formula (Interest = Total accrued amount—Principal amount).

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