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General ScienceSimple & Compound Interest

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A sum of $5000 amounts to$ 6050 in 2 years at compound interest. What is the rate of interest per annum?

10%

12%

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral ScienceSimple & Compound Interest

Option C

10%

Quick Summary:

Compound interest represents the accumulation of interest on both the principal and the previously accumulated interest. In this case, the amount $A$ grows from $P$ to $A$ over $n$ years, following the geometric progression defined by the compound interest formula.

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of it like a snowball rolling down a hill: it picks up more snow as it gets larger, just as interest earns more interest the longer it sits in the account.

🔢 Key Formulas

$A = P(1 + \frac{R}{100})^n$ — Compound Amount formula

$CI = A - P$ — Compound Interest formula

⚙️ Working Principle

The principle operates on the mechanism of exponential growth where the principal increases by a factor of $(1 + \frac{R}{100})$ each year. By rearranging $A = P(1 + \frac{R}{100})^n$ , we isolate the rate $R$ using the square root method since $n=2$ . This demonstrates the concept of time-value of money where interest compounds over time.

📌 Key Points

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The rate of interest is applied to the accumulated balance, not just the initial principal.
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For $n=2$ , the ratio $\frac{A}{P}$ is the square of the growth factor $(1 + \frac{R}{100})$ .
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Compounding frequency significantly affects the final maturity amount.

✅ Advantages

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Maximizes returns over long periods.
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Accounts for the time-value of money.

❌ Disadvantages / Limitations

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Increases the burden of debt for borrowers.
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Less intuitive than simple interest calculation.

🛠️ Applications / Uses

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Banking and financial savings accounts.
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Investment growth projections in economics.

📄 Additional Information

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Given $P = 5000$ , $A = 6050$ , $n = 2$ . Then $6050 = 5000(1 + \frac{R}{100})^2$ . Simplifying, $\frac{6050}{5000} = 1.21$ . Taking the square root of $1.21$ gives $1.1$ , implying $\frac{R}{100} = 0.1$ , so $R = 10\%$ .
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Option A (8%) results in $5000 \times (1.08)^2 = 5832$ . Option B (9%) results in $5000 \times (1.09)^2 = 5934.5$ . Option D (12%) results in $5000 \times (1.12)^2 = 6272$ .

📊 Diagram / Illustration

✅

C is correct — The calculation reveals that a 10% annual interest rate applied over 2 years results in the exact maturity value of 6050.

Core Concepts Used

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Exponential Growth Compound Interest Geometric Progression

💡 EXAM TIP

When $n=2$ , always look for a perfect square in the ratio $\frac{A}{P}$ to quickly identify the growth factor $(1 + \frac{R}{100})$ .

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