Difference Between Simple Interest And Compound Interest (Bonus: Solved QnAs)

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Grasping the difference between simple interest and compound interest is crucial in financial decision-making. Simple interest involves calculating interest solely on the principal amount, while compound interest considers both the principal and accrued interest. By comprehending these concepts, individuals can make informed choices to optimize their financial outcomes.

Defining Interest Types

To begin with, let us understand the definitions of interest types in detail:

Simple Interest

Simple interest is a direct method of calculating interest, commonly used for short-term loans or investments. It is calculated solely on the principal amount without considering any previously earned interest.

Formula: S.I. = (P × T × R) ⁄ 100

For example, if you borrow ₹1000 at a simple interest rate of 5% per year, you will pay ₹50 in interest annually.

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.

Compound Interest

Compound interest involves calculating interest on both the principal amount and any accumulated interest. This results in a snowball effect where your money grows faster over time compared to simple interest.

Formula: C.I. = P(1+r⁄n)^nt

For instance, if you invest ₹1000 at an annual compound interest rate of 5%, your investment will not only earn ₹50 in the first year but also additional earnings on that ₹50 in subsequent years.

When you invest or borrow using compound interest, you earn or pay interest not just on the initial sum but also on any previously earned or charged interest.

Simple Interest Vs. Compound Interest

Let us now see the basic difference between simple interest and compound interest:

Click here to enhance and upskill your quantitative aptitude in simple and compound interest right away!

Selected Solved Questions & Answers

Below are some selected and solved questions and answers related to simple and compound interest. Practice and improve your knowledge in a consistent manner:

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 = (5000 x 3 x 2)/ 100

= 30000 / 100

= 300

Therefore, the simple interest earned on a principal amount of ₹5000 at an interest rate of 3% per annum for a period of 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

= 500 x 8 x 3 / 100

= 120

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

Question 4: If ₹5000 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 = 5000 x 0.06 x 3= 900

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

Question 5: John invested ₹5000 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 = 5000 x 5% = ₹250

Amount after first year = 5000 + 250 = ₹5250

Second-year interest = 5250 x 7% = ₹367.50

Amount after second year = 5250 + 367.50 =₹5617.50

Third-year interest = 5617.50 x 10% = ₹561.75

Total amount after third year = 5617.50 + 561.75 = ₹6179.25

Therefore, John had ₹6179.25 in his account at the end of the third year.

Question 6: If you invest ₹5000 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 = ₹5000

r=5%=5/100=0.05

n=1 (interest compounded annually)

t=5 years

A=5000×(1+0.05/1​)^(1×5)

  =5000×(1.05)⁵

A=5000×(1.27628)

A≈6381.40

So, after 5 years, you would have approximately ₹6381.40 in the account.

Question 7. If you invest ₹8000 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 = ₹8000
• r=4%=0.04 (decimal)
• n=2 (interest compounded semi-annually)
• t=3 years

Putting these values into the formula:

A=8000×(1+0.04/2​)^(2×3)

A=8000×(1.02)6

Now, calculate A:

A=8000×(1.126825)

A≈9014.60

So, after 3 years, you would have approximately ₹9014.60 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=10000×(1+0.06/4​)^(4×7)

A=10000×(1+0.06/4​)²⁸

A=10000×(1.015)²⁸

A≈10000×(1.662792)

A≈16627.92

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

Question 9: You decide to invest ₹15,000 with an annual interest rate of 8%, compounded monthly. However, after 3 years, you decide to add an additional ₹5,000 to the account. Assuming the same interest rate and compounding frequency, how much money will you have after a total of 6 years?

Solution: Let's first calculate the amount accumulated after 3 years. As per the question, 

• Initial investment P₁​= ₹15,000
• Annual interest rate r = 8% = 0.08
• Compounding frequency n = 12 (monthly compounding)
• Time t₁​= 3 years

Using the compound interest formula:

A_1​=P1​×(1+r/n​)^nt_1​

A₁​=15000×(1+0.08​/12)^(12×3)

A_1​≈15000×(1+0.08/12​)³⁶

A₁​≈15000×(1.0066667)³⁶

A₁​≈15000×(1.2653166)

A₁​≈18979.75

After 3 years, the accumulated amount is approximately ₹18,979.75.

Now, let's calculate the amount accumulated after 6 years, considering the additional ₹5,000 investment:

Given:

• Additional investment P₂​ = ₹5,000
• Time t_2​ = 6 years (including the initial 3 years)

Using the compound interest formula again:

A₂​=(A1​+P2​)×(1+r/n​)^nt2​

A_2​=(18979.75+5000)×(1+0.08/12​)^(12×3)

A₂​≈23979.75×(1+0.08​/12)⁷²

A₂​≈23979.75×(1.0066667)⁷²

A₂​≈23979.75×(1.718901)

A₂​≈41205.22

After 6 years, including the additional investment, the accumulated amount would be approximately ₹41,205.22.

Question 10: You invest ₹20,000 in an account with an annual interest rate of 7%, compounded quarterly. After 2 years, you withdraw ₹5,000 from the account. Assuming the same interest rate and compounding frequency, how much money will you have after 5 years from the initial investment?

Solution: 

Let's start by calculating the amount accumulated after 2 years:

Given:

• Initial investment P₁​ = ₹20,000
• Annual interest rate r = 7% = 0.07 (decimal)
• Compounding frequency n = 4 (quarterly compounding)
• Time t₁​ = 2 years

Using the compound interest formula:

A_1​=P_1​×(1+r/n​)^nt1​

A₁​=20000×(1+0.07​/4)^(4×2)

A₁​≈20000×(1+40.07​)⁸

A₁≈20000×(1.0175)⁸

A₁≈20000×(1.14156011)

A₁≈22831.20

After 2 years, the accumulated amount is approximately ₹22,831.20.

Now, you withdraw ₹5,000 from the account, leaving P₂ = 20000 - 5000 = ₹15,000 as the new principal.

Next, let's calculate the amount accumulated after the remaining 3 years:

Given:

• Principal P₂ = ₹15,000
• Annual interest rate r = 7% = 0.07 (decimal)
• Compounding frequency n = 4 (quarterly compounding)
• Time t₂​ = 3 years

Using the compound interest formula:

A₂​=P₂​×(1+r/n​)^nt2​

A₂=15000×(1+0.07/4​)^(4×3)

A₂≈15000×(1+0.07​/4)¹²

A₂​≈15000×(1.0175)¹²

A₂≈15000×(1.30773342471)

A₂≈19615.00

After 3 additional years, the accumulated amount from the remaining ₹15,000 is approximately ₹19,615.00.

So, after a total of 5 years from the initial investment, you would have approximately ₹19,615.00 in the account.

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Conclusion

Being aware of the difference between simple interest and compound interest enables one to see how each type impacts financial outcomes. Simple interest offers straightforward calculations, while compound interest has the potential for exponential growth over time. 

By grasping these concepts, individuals can make informed decisions regarding finance, investments, loans, or savings. Embracing a detailed understanding of simple and compound interest empowers individuals to optimize their financial strategies for long-term success.

Frequently Asked Questions (FAQs)

1. Point out the key difference between simple interest and compound interest.

Simple interest is calculated only on the principal amount, while compound interest includes both the principal and accumulated interest. Compound interest grows faster due to earning interest on previously earned interest.

2. How is simple interest calculated?

To calculate simple interest, you multiply the principal amount by the interest rate and the time period using the formula: Interest = Principal x Rate x Time.

3. Can you explain how compound interest works in practice?

Compound interest involves reinvesting earned interest back into the principal amount. Over time, this leads to exponential growth as each period's earnings contribute to the next period's calculations.

4. What are compounding periods in compound interest?

Compounding periods refer to how often the interest is added to the principal amount. The more frequent compounding occurs within a given timeframe, such as monthly or daily compounding, the higher the effective yield will be.

5. When should one choose between simple and compound interest?

Choose simple interest for short-term loans or when you prefer straightforward calculations. Opt for compound interest for long-term investments or savings goals where maximizing growth over time is crucial. Consider factors like time horizon and financial objectives when deciding between them.

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