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MathematicsArithmetic Aptitude

A sum of money doubles itself in 5 years at simple interest · What is the rate of interest per annum?

$10\%$

$20\%$

$15\%$

$25\%$

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsArithmetic Aptitude

Option B

$20\%$

Quick Summary:

Given: Sum of money doubles itself (Amount = 2 * Principal) in Time = 5 years at simple interest.

📐MAMath SolutionDirect Formula

📋 Given

Sum of money doubles itself (Amount = 2 * Principal) in Time = 5 years at simple interest.

🔢 Formula Used

R=(n−1)×100TR = \frac{(n-1) \times 100}{T}R=T(n−1)×100​

⚡ Exam Hall Shortcut / Speed Trick

For a sum to double, the interest equals the principal · Simply divide 100% by the number of years: $100 / 5 = 20\%$ .

⚠️ Common Student Trap / Pitfall

Students often mistake the final amount (2P) for the interest earned (P) and calculate incorrectly using $200$ instead of $100$ in the numerator.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define the relationship

Let the Principal be $P$ . If the money doubles, the Amount $A = 2P$ . Therefore, Simple Interest $SI = A - P = 2P - P = P$ .

SI=PSI = PSI=P

Apply Simple Interest formula

The formula for simple interest is $SI = \frac{P \times R \times T}{100}$ . Substituting $SI = P$ and $T = 5$ years.

P=P×R×5100P = \frac{P \times R \times 5}{100}P=100P×R×5​

Solve for Rate (R)

Cancel $P$ from both sides: $1 = \frac{5R}{100}$ . Solving for $R$ gives $R = \frac{100}{5} = 20\%$ .

R=20%R = 20\%R=20%

✅

B is correct because the interest earned equals the principal in 5 years, necessitating a 20% rate per annum to satisfy the simple interest formula.

Core Concepts Used

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💡 EXAM TIP

This logic is identical to 'Time and Work' problems where $1$ unit of work is completed in $T$ time, meaning the rate of work is $1/T$ per unit time.

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