The difference between Simple Interest and Compound Interest o... | General Science MCQ | Examoogle

General ScienceSimple & Compound Interest

The difference between Simple Interest and Compound Interest on a certain sum of money for 2 years at 10% per annum is Rs 50. What is the sum?

4000

5000

6000

7000

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral ScienceSimple & Compound Interest

Option B

5000

Quick Summary:

The difference between Compound Interest (CI) and Simple Interest (SI) for a period of 2 years is generated by the interest earned on the interest from the first year. For a sum $P$ at a rate $r\%$ , this difference is given by the formula $D = P \times (\frac{r}{100})^2$ .

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💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of Simple Interest as a fixed salary, whereas Compound Interest is like a snowball rolling down a hill; as it gathers snow (interest), its surface area increases, allowing it to collect even more snow in the next rotation.

🧠 Memory Mnemonic / Shortcut Aid

Remember 'CI-SIDiff = P(R/ $100)^2$ ' for 2 years.

🔢 Key Formulas

$D = P \times (\frac{r}{100})^2$ — The formula for the difference between CI and SI over 2 years

$SI = \frac{P \times R \times T}{100}$ — The formula for simple interest

$CI = P(1 + \frac{r}{100})^n - P$ — The formula for compound interest

⚙️ Working Principle

In Simple Interest, the principal amount remains constant, meaning interest is only calculated on the initial sum. In Compound Interest, the interest earned at the end of the first year is added to the principal for the second year, creating an additional layer of growth. The difference $D$ specifically represents the interest accrued on the first year's interest, mathematically expressed as $P \times (\frac{r}{100}) \times (\frac{r}{100})$ .

📌 Key Points

▸
The difference between CI and SI for 2 years is always $P(r/100)^2$ .
▸
At 10% rate, the first year interest is 10% of P, and the interest on that interest is 10% of 10% of P, which equals 1% of P.
▸
Given the difference is 50, then $0.01 \times P = 50$ , so $P = 5000$ .

✅ Advantages

▸
The difference formula allows for rapid calculation without finding the total CI or SI amounts separately.

❌ Disadvantages / Limitations

▸
This specific shortcut formula is valid only for a duration of 2 years.

🛠️ Applications / Uses

▸
Banking sector for calculating yield differences
▸
Financial investment analysis

📄 Additional Information

▸
Rate $r = 10\%$ , Difference $D = 50$ , Time $t = 2$ years.
▸
Option A is incorrect because $4000 \times (0.1)^2 = 40$ . Option C is incorrect because $6000 \times (0.1)^2 = 60$ . Option D is incorrect because $7000 \times (0.1)^2 = 70$ .

📊 Diagram / Illustration

✅

B is correct — Using the formula $50 = P \times (\frac{10}{100})^2$ , we find $P = 5000$ .

Core Concepts Used

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Principal sum Rate of interest Time duration Compounding effect

💡 EXAM TIP

For 3 years, the difference formula becomes $D = P(r/100)^2 \times (3 + r/100)$ . Always check the number of years before applying shortcut formulas.

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